Advanced management accounting Essay Example | Topics and Well Written Essays - 1500 words - 1

Advanced management accounting - Essay Example This will help the management in adopting corrective measure. This also includes administrative control which involves laws, regulations, norms, standard procedures. The second category deals with personal control, social control and behavioural control. Management control system serves as language and helps in communication system. Management control system also plays the role of transfer pricing for performing the strategic functions of the organization. Management control system can be effectively designed and implemented if there is dedication and commitment in the top level executives (Giraud, Zarlowski, Saulpic, Lorain, Fourcade and Morales, 2007). The less involvement, less initiative and also less interest in the activities among the top level executives will lead the top management in diverting its attention to other areas, which is not suitable for the smooth running of the organization. The Organization’s which completes there project in time establishes its budget and fulfilment of the maintenance of quality is considered as a successful company or organization (NOEVERMAN, 2007). Therefore if the organization is not able to complete its project in time can lead or act as a challenge for delivery of project in time. Lack of cross – functional communication Effective communication is a main function for exchanging of information between the people in the organization. It serves as a source for exchanging of ideas (Arsh, 2010). The changes that are adopted in the organization have to be clearly communicated among the persons in the organization and also provide the rationale for the changes undergone by the organization (Neale & McElroy, 2004). The organization must clearly define the benefits that the organization expects from the project and the challenges or obstacles towards receiving those benefits (Malmi &

Bio-ethics Essay Example | Topics and Well Written Essays - 250 words

Bio-ethics - Essay Example Following a close analysis on the issue, I think that surgeon’s desire for fame has no effect on their work. To begin with, surgeons are human beings although they have an extra ordinary gift and therefore their desire for fame is human nature and therefore has no negative effect on their work. Their desire for fame only contributes to confidence on their work with little or no effect on the patient’s wellbeing. Secondly, Surgeons are trained persons who value their profession and therefore their desire for fame is for personal interest with little or no effect on their patient. Becoming a surgeon is not an easy affair since they have to go through intensive and extensive training before qualifying for the job. This makes them value their job and patients more than any other personal desire such as fame. Fame is not given but earned and most surgeons would agree with this fact, this implies that a surgeon who desires to have fame must strive to earn it through genuine methods (Scott 101). The only possible genuine method through which surgeons can earn the much-needed fame is by improving the care they give to their patients and this has no interference on a patient’s

Personality Factors for a Leader

Personality Factors for a Leader Nature of Leadership: Laurie J. Mullins states that Leadership is a relationship through which one person influences the behavior or actions of other people (Mullins 2010: 373). He says that Leadership is all about determination, personality and innate ability at the right time for a particular competitive situation. Many effective business leaders have no formal academic qualifications and each has their own individual leadership style. Leaders can motivate their followers and can design organizational contexts and make them function effectively. Criterion of leadership: Though there are lot many criterion for leadership, we in our group selected a few of them. VISION: A good leader should work hard at communicating their vision for the organization to all staff at all levels. He has to understand that their vision must appeal to the staff at both an emotional and practical level. Basically a leader has to understand the culture and values of his organization and its impact on its future development. He has to recognize blind alleys. MOTIVATION: A leader has to understand that every member has a different set of motivational stimuli, motivate them accordingly. He has to explain his decisions in terms of their benefit to the organization and its members. Most importantly a leader has to find out the flaws if any or celebrate and reward individual and team achievements. EMPOWEREMENT: An empowered leader should believe that people generally respond well when given greater responsibility for their own performance without disturbing the organizations model. For that he has to allocate sufficient resources to training and development and get a buzz when staff set and achieve their own goals. He should realize that the organization would still function if you were not there. COMMUNICATIONS: One of the most important criteria for a leader is communication skill. He has to use his communication influence to encourage two way communications at all levels in your organization. He has to encourage personal contact rather than written, mechanical or technological alternatives. Finally has to encourage a diversity of opinion and constructive criticism and walk the talk. RELATIONSHIPS: A successful leader should work hard at countering a them and us culture within your organization and maintain relationships inside and outside his team. He has to set clear codes of acceptable conduct and take action against breaches of them and stress that everyone contributes to the success of the team(s) they belong to. One of the most important qualities of a leader is that he should be able to admit a mistake when you make it. EMOTIONAL INTELLIGENCE: Mullins describes emotional intelligence as abilities such as being able to motivate oneself and persist in the face of frustrations; to control impulse and delay gratification; to regulate ones moods and keep distress from swamping the ability to think; to empathize and to hope. (Mullins 2010: 144). Emotional intelligence is the ability to think, handle situations either in frustrations or success emotionally. A leader should have this emotional intelligence so as to lead his team in critical situations. ATTITUDE: Attitudes are learned throughout life and are embodied within socialization process. They can be defined as providing a state of readiness or tendency to respond in a particular ways.(Mullins 2010: 145). A result oriented leader should have knowledge, should be expressive, should be instrumental, and ego defensive. TEAMWORK: A good leader is the one who has to create an understanding of working in groups and teams. It is necessary for him to recognize the nature of human relationships, functions, roles and factors that influence team performance and effectiveness. TIME MANAGEMENT: Time management is one of the key factors for a good leader. They should not only manage their own time but also manage their staff or teams time. They have to establish key tasks, set objectives, identify performance standards, check for constraints and decide on action plans. PROBLEM SOLVING SKILLS: Problem-solving is the removal of the barrier. A result- oriented leader should have good problem solving skills as the success of his mission depends on the problems they face and the way he solve. It may be an internal weakness, or any external threat. Group Feedback and My Capabilities: The group members in our group say that I have good visionary qualities and they say that I always plan for the future. I think that whatever plan I am making should be useful not only to me but for others and my plan should be like a generalized theory and have proofs. Coming to motivation, our group members feel that I can motivate them with my verbal skills and also induce confidence into them. One of the group member reviews me that I also reward and always give them a good feedback. My group members have trust on me and are able to rely on me and I feel that I have good empowerment skills. Whenever I lead them I dont feel authoritative rather I feel responsible which makes me a successful leader. I feel that empowerment should not be taken by yourself; members around you should choose you. I use my verbal skills and my body language in an effective manner so as to put on my thought in front of them. They will be always encouraged and convinced with my presentation skills and so I can make use them for the maximum extent so as to accomplish our mission. In any context whether it may be in formal situations, informal situations, in an organization, in completing a group activity, I feel the most important part is maintaining relations within a group. I have won my group members and they vote me positively in these criteria. I feel that as a leader, whatever I do should be convinced among my group members and the plan should be transparent. I feel that no group member should be in dark side. One of my group members states that I possess a bit low emotional intelligence. I dont agree with them completely because there are no such relevant situations where I got a chance to exhibit them. I have a few real time examples where I was chosen to convince people and I succeeded i n that. When coming to attitude, each person in our group has different viewpoints regarding this criterion. One says that I am egoistic. It might not be a false judgment but its true in some issues. I am a bit EGOISTIC person, but the way I exhibit it depends on the situations and circumstances.one more member in our group says that I calm down when things doesnt go well and look for a chance or a solution. That is also true and it happens most of the time when handling worthless issues. The other member says that my attitude is good and positive always. I feel that attitude varies accordingly with peoples mindset and it is the way how they receive. Team playing is one of the best qualities which I possess. My group members also agree with this statement. They say that I am always ready to help them irrelevant of the situation. I feel that in a team di Coming to time management, I am a bit lazy person which is a drawback for being a leader. But my group members except one, praise me that I am good at managing time. May be, only one member found out my drawback and it is true. Actual reason is I need a small push up to start of my work which I am trying to rectify it. I am good at allocating time resources but poor at implementing it within given constraints. When I deal with any problematic situations, I come out of the situation and analyze the problem, find the causes, starting from the basics, question myself and solve the problem and my group members accessed me the same. But I feel every time that I have to improve my problem solving skills. I dont get satisfied at any point of time and thinks of a better way to solve a problem. I give feedback to myself most of the time. Conclusion: Overall there are lots of important qualities like VISION, MOTIVATION, RELATIONSHIPS, and COMMUNICATION SKILLS in me which make me to emerge as a successful leader, though I have a few qualities like ATTITUDE, TIME MANAGEMENT which needs to be improved. In this present scenario one should have to develop lot many qualities other than these mentioned and emerge out as a Good Leader in this changing world.

Charles dikenson biography :: essays research papers fc

Charles Dickens Biography   Ã‚  Ã‚  Ã‚  Ã‚  Charles Dickens was one of the most popular writers of all time. Dickens was very observant of life, and had a great understanding of humanity.   Ã‚  Ã‚  Ã‚  Ã‚  Charles John Huffam Dickens was born in Portsmouth, England, on February 7, 1812. When he was two years old he and his family moved to London. Dickens father, John Dickens, was a poor clerk who worked for the navy, and he also spent time in prison for debt. When John was not in prison he lacked the money to adequately support his family. When Charles was twelve he worked in a London factory. That job was so miserable that the misery of the experience stayed with him his whole life. Dickens became a newspaper reporter in the late 1820’s. He specialized in covering debates in Parliament and also wrote feature articles. This helped him develop his skill portraying his character’s speech realistically. His first book was â€Å"Sketches by Boz† in 1836; it consisted of articles he wrote for monthly magazine. The book that got him famous was â€Å"The Posthumous Papers of the Pickwick Club. This book describes the adventures and misadventures of a group of people in an English countryside. Dickens founded and edited two highly successful magazines. Those magazines were â€Å"Household Words† and â€Å"All Year Round†. Dickens was always in the news, and was honored, and recognized everywhere he went. In 1836 Dickens married Catherine Hogarth. Catherine had a sister named Mary, who died in 1837. Dickens grieved so much over her death that some people believe that he loved her more then he loved Catherine. Catherine was a good wife but she wasn’t a very intelligent woman. She an Dickens had ten children, and separated in 1858. Dickens had a vast amount of physical and mental energy. He had so much energy that he could record all of his activities and make it interesting to read. Dickens had a life other than writing. He spent much of his free time with his friends from the worlds of art and literature. He also enjoyed drama. He went to the theater as often as he could. When he was rich and famous, he produc ed and acted in amateur theatrical productions. Dickens was also a giving person. When he was not socializing or in the theater, he was giving to various charities. These charities included giving money toward build schools for the poor school children and loans that enabled the poor to move to Australia.

Accrual Swaps

ACCRUAL SWAPS AND RANGE NOTES PATRICK S. HAGAN BLOOMBERG LP 499 PARK AVENUE NEW YORK, NY 10022 [email  protected] NET 212-893-4231 Abstract. Here we present the standard methodology for pricing accrual swaps, range notes, and callable accrual swaps and range notes. Key words. range notes, time swaps, accrual notes 1. Introduction. 1. 1. Notation. In our notation today is always t = 0, and (1. 1a) D(T ) = today’s discount factor for maturity T. For any date t in the future, let Z(t; T ) be the value of $1 to be delivered at a later date T : (1. 1b) Z(t; T ) = zero coupon bond, maturity T , as seen at t. These discount factors and zero coupon bonds are the ones obtained from the currency’s swap curve. Clearly D(T ) = Z(0; T ). We use distinct notation for discount factors and zero coupon bonds to remind ourselves that discount factors D(T ) are not random; we can always obtain the current discount factors from the stripper. Zero coupon bonds Z(t; T ) are random, at least until time catches up to date t. Let (1. 2a) (1. 2b) These are de? ned via (1. 2c) D(T ) = e? T 0 f0 (T ) = today’s instantaneous forward rate for date T, f (t; T ) = instantaneous forward rate for date T , as seen at t. f0 (T 0 )dT 0 Z(t; T ) = e? T t f (t,T 0 )dT 0 . 1. 2. Accrual swaps (? xed). ?j t0 t1 t2 †¦ tj-1 tj †¦ tn-1 tn period j Coupon leg schedule Fixed coupon accrual swaps (aka time swaps) consist of a coupon leg swapped against a funding leg. Suppose that the agreed upon reference rate is, say, k month Libor. Let (1. 3) t0 < t1 < t2  ·  ·  · < tn? 1 < tn 1 Rfix Rmin Rmax L( ? ) Fig. 1. 1. Daily coupon rate be the schedule of the coupon leg, and let the nominal ? xed rate be Rf ix . Also let L(? st ) represent the k month Libor rate ? xed for the interval starting at ? st and ending at ? end (? st ) = ? t + k months. Then the coupon paid for period j is (1. 4a) where (1. 4b) and (1. 4c) ? j = #days ? st in the interval with Rmin ? L(? st ) ? Rmax . Mj ? j = cvg(tj? 1 , tj ) = day count fraction for tj? 1 to tj , Cj = ? j Rf ix ? j paid at tj , Here Mj is the total number of days in interval j, and Rmin ? L(? st ) ? Rmax is the agreed-upon accrual range. Said another way, each day ? st in the j th period contibutes the amount ? ?j Rf ix 1 if Rmin ? L(? st ) ? Rmax (1. 5) 0 otherwise Mj to the coupon paid on date tj . For a standard deal, the leg’s schedule is contructed like a standard swap schedule. The theoretical dates (aka nominal dates) are constructed monthly, quarterly, semi-annually, or annually (depending on the contract terms) backwards from the â€Å"theoretical end date. † Any odd coupon is a stub (short period) at the front, unless the contract explicitly states long ? rst, short last, or long last. The modi? ed following business day convention is used to obtain the actual dates tj from the theoretical dates. The coverage (day count fraction) is adjusted, that is, the day count fraction for period j is calculated from the actual dates tj? 1 and tj , not the theoretical dates. Also, L(? t ) is the ? xing that pertains to periods starting on date ? st , regardless of whether ? st is a good business day or not. I. e. , the rate L(? st ) set for a Friday start also pertains for the following Saturday and Sunday. Like all ? xed legs, there are many variants of these coupon legs. The only variations that do not make sense for coupon legs are â€Å"set-in-arrearsâ €  and â€Å"compounded. † There are three variants that occur relatively frequently: Floating rate accrual swaps. Minimal coupon accrual swaps. Floating rate accrual swaps are like ordinary accrual swaps except that at the start of each period, a ? ating rate is set, and this rate plus a margin is 2 used in place of the ? xed rate Rf ix . Minimal coupon accrual swaps receive one rate each day Libor sets within the range and a second, usually lower rate, when Libor sets outside the range ? j Mj ? Rf ix Rf loor if Rmin ? L(? st ) ? Rmax . otherwise (A standard accrual swap has Rf loor = 0. These deals are analyzed in Appendix B. Range notes. In the above deals, the funding leg is a standard ?oating leg plus a margin. A range note is a bond which pays the coupon leg on top of the principle repayments; there is no ? oating leg. For these deals, the counterparty’s credit-worthiness is a key concern. To determine the correct value of a range note, one needs to use an option adjusted spread (OAS) to re? ect the extra discounting re? ecting the counterparty’s credit spread, bond liquidity, etc. See section 3. Other indices. CMS and CMT accrual swaps. Accrual swaps are most commonly written using 1m, 3m, 6m, or 12m Libor for the reference rate L(? st ). However, some accrual swaps use swap or treasury rates, such as the 10y swap rate or the 10y treasury rate, for the reference rate L(? st ). These CMS or CMT accrual swaps are not analyzed here (yet). There is also no reason why the coupon cannot set on other widely published indices, such as 3m BMA rates, the FF index, or the OIN rates. These too will not be analyzed here. 2. Valuation. We value the coupon leg by replicating the payo? in terms of vanilla caps and ? oors. Consider the j th period of a coupon leg, and suppose the underlying indice is k-month Libor. Let L(? st ) be the k-month Libor rate which is ? xed for the period starting on date ? st and ending on ? end (? st ) = ? st +k months. The Libor rate will be ? xed on a date ? f ix , which is on or a few days before ? st , depending on currency. On this date, the value of the contibution from day ? st is clearly ? ? ? j Rf ix V (? f ix ; ? st ) = payo? = Z(? f ix ; tj ) Mj ? 0 if Rmin ? L(? st ) ? Rmax otherwise (2. 1) , where ? f ix the ? xing date for ? st . We value coupon j by replicating each day’s contribution in terms of vanilla caplets/? oorlets, and then summing over all days ? st in the period. Let Fdig (t; ? st , K) be the value at date t of a digital ? oorlet on the ? oating rate L(? st ) with strike K. If the Libor rate L(? st ) is at or below the strike K, the digital ? oorlet pays 1 unit of currency on the end date ? end (? st ) of the k-month interval. Otherwise the digital pays nothing. So on the ? xing date ? f ix the payo? is known to be ? 1 if L(? st ) ? K , (2. 2) Fdig (? f ix ; ? st , K) = Z(? f ix ; ? end ) 0 otherwise We can replicate the range note’s payo? for date ? st by going long and short digitals struck at Rmax and Rmin . This yields, (2. 3) (2. 4) ? j Rf ix [Fdig (? f ix ; ? st , Rmax ) ? Fdig (? f ix ; ? st , Rmin )] Mj ? ?j Rf ix 1 = Z(? f ix ; ? end ) 0 Mj 3 if Rmin ? L(? st ) ? Rmax . otherwise This is the same payo? as the range note, except that the digitals pay o? on ? end (? st ) instead of tj . 2. 1. Hedging considerations. Before ? ing the date mismatch, we note that digital ? oorlets are considered vanilla instruments. This is because they can be replicated to arbitrary accuracy by a bullish spread of ? oorlets. Let F (t, ? st , K) be the value on date t of a standard ? oorlet with strike K on the ? oating + rate L(? st ). This ? oorlet pays ? [K ? L(? st )] on the end date ? end (? st ) of the k-m onth interval. So on the ? xing date, the payo? is known to be (2. 5a) F (? f ix ; ? st , K) = ? [K ? L(? st )] Z(? f ix ; ? end ). + Here, ? is the day count fraction of the period ? st to ? end , (2. 5b) ? = cvg(? st , ? end ). 1 ? oors struck at K + 1 ? nd short the same number struck 2 The bullish spread is constructed by going long at K ? 1 ?. This yields the payo? 2 (2. 6) which goes to the digital payo? as ? > 0. Clearly the value of the digital ? oorlet is the limit as ? > 0 of (2. 7a) Fcen (t; ? st , K, ? ) = ? 1  © F (t; ? st , K + 1 ? ) ? F (t; ? st , K ? 1 ? ) . 2 2 ? 1  © F (? f ix ; ? st , K + 1 ? ) ? F (? f ix ; ? st , K ? 1 ? ) 2 2 ? ? ? ? 1 ? 1 = Z(? f ix ; ? end ) K + 1 ? ? L(? st ) 2 ? ? ? 0 if K ? 1 ? < L(? st ) < K + 1 ? , 2 2 if K + 1 ? < L(? st ) 2 if L(? st ) < K ? 1 ? 2 Thus the bullish spread, and its limit, the digitial ? orlet, are directly determined by the market prices of vanilla ? oors on L(? st ). Digital ? oorlets may develop an unbounded ? - risk as the ? xing date is approached. To avoid this di? culty, most ? rms book, price, and hedge digital options as bullish ? oorlet spreads. I. e. , they book and hedge the digital ? oorlet as if it were the spread in eq. 2. 7a with ? set to 5bps or 10bps, depending on the aggressiveness of the ? rm. Alternatively, some banks choose to super-replicate or sub-replicate the digital, by booking and hedging it as (2. 7b) or (2. 7c) Fsub (t; ? st , K, ? ) = 1 {F (t; ? st , K) ? F (t; ? st , K ? ?)} Fsup (t; ? st , K, ? ) = 1 {F (t; ? st , K + ? ) ? F (t; ? st , K)} depending on which side they own. One should price accrual swaps in accordance with a desk’s policy for using central- or super- and sub-replicating payo? s for other digital caplets and ? oorlets. 2. 2. Handling the date mismatch. We re-write the coupon leg’s contribution from day ? st as ? ?j Rf ix Z(? f ix ; tj ) ? V (? f ix ; ? st ) = Z(? f ix ; ? end ) Mj Z(? f ix ; ? end ) ? 0 4 (2. 8) if Rmin ? L(? st ) ? Rmax otherwise . f(t,T) L(? ) tj-1 ? tj ? end T Fig. 2. 1. Date mismatch is corrected assuming only parallel shifts in the forward curve The ratio Z(? ix ; tj )/Z(? f ix ; ? end ) is the manifestation of the date mismatch. To handle this mismatch, we approximate the ratio by assuming that the yield curve makes only parallel shifts over the relevent interval. See ?gure 2. 1. So suppose we are at date t0 . Then we assume that (2. 9a) Z(? f ix ; tj ) Z(t0 ; tj ) ? [L(? st )? Lf (t0 ,? st )](tj en d ) = e Z(? f ix ; ? end ) Z(t0 ; ? end ) Z(t0 ; tj ) = {1 + [L(? st ) ? Lf (t0 , ? st )](? end ? tj ) +  ·  ·  · } . Z(t0 ; ? end ) Z(t0 ; ? st ) ? Z(t0 ; ? end ) + bs(? st ), ? Z(t0 ; ? end ) Here (2. 9b) Lf (t0 , ? st ) ? is the forward rate for the k-month period starting at ? t , as seen at the current date t0 , bs(? st ) is the ? oating rate’s basis spread, and (2. 9c) ? = cvg(? st , ? end ), is the day count fraction for ? st to ? end . Since L(? st ) = Lf (? f ix , ? st ) represents the ? oating rate which is actually ? xed on the ? xing date ? ex , 2. 9a just assumes that any change in the yield curve between tj and ? end is the same as the change Lf (? f ix , ? st ) ? Lf (t0 , ? st ) in the reference rate between the observation date t0 , and the ? xing date ? f ix . See ? gure 2. 1. We actually use a slightly di? erent approximation, (2. 10a) where (2. 10b) ? = ? end ? tj . ? end ? ? st Z(? ix ; tj ) Z(t0 ; tj ) 1 + L(? st ) ? Z(? f ix ; ? end ) Z(t0 ; ? end ) 1 + Lf (t0 , ? st ) We prefer this approximation because it is the only linear approximation which accounts for the day count basis correctly, is exact for both ? st = tj? 1 and ? st = tj , and is centerred around the current forward value for the range note. 5 Rfix Rmin L0 Rmax L(? ) Fig. 2. 2. E? ective contribution from a single day ? , after accounting for the date mis-match. With this approximation, the payo? from day ? st is ? 1 + L(? st ) (2. 11a) V (? f ix ; ? ) = A(t0 , ? st )Z(? f ix ; ? end ) 0 as seen at date t0 . Here the e? ctive notional is (2. 11b) A(t0 , ? st ) = if Rmin ? L(? st ) ? Rmax otherwise 1 ? j Rf ix Z(t0 ; tj ) . Mj Z(t0 ; ? end ) 1 + Lf (t0 , ? st ) We can replicate this digital-linear-digital payo? by using a combination of two digital ? oorlets and two standard ? oorlets. Consider the combination (2. 12) V (t; ? st ) ? A(t0 , ? st ) {(1 + Rmax )Fdig (t, ? st ; Rmax ) ? (1 + ? Rmin )Fdig (t, ? st ; Rmin ) F (t, ? st ; Rmax ) + ? F (t, ? st ; Rmi n ). Setting t to the ? xing date ? f ix shows that this combination matches the contribution from day ? st in eq. 2. 11a. Therefore, this formula gives the value of the contribution of day ? t for all earlier dates t0 ? t ? ? f ix as well. Alternatively, one can replicate the payo? as close as one wishes by going long and short ? oorlet spreads centerred around Rmax and Rmin . Consider the portfolio (2. 13a) A(t0 , ? st )  © ? V (t; ? st , ? ) = a1 (? st )F (t; ? st , Rmax + 1 ? ) ? a2 (? st )F (t; ? st , Rmax ? 1 ? ) 2 2 ? 1 ? a3 (? st )F (t; ? st , Rmin + 2 ? )+ a4 (? st )F (t; ? st , Rmin ? 1 ? ) 2 a1 (? st ) = 1 + (Rmax ? 1 ? ), 2 a3 (? st ) = 1 + (Rmin ? 1 ? ), 2 ? ? a2 (? st ) = 1 + (Rmax + 1 ? ), 2 a4 (? st ) = 1 + (Rmin + 1 ? ). 2 with (2. 13b) (2. 13c) Setting t to ? ix yields (2. 14) ? V = A(t0 , ? st )Z(? f ix ; ? end ) 0 if L(? st ) < Rmin ? 1 ? 2 1 + L(? st ) if Rmin + 1 ? < L(? st ) < Rmax ? 1 ? , 2 2 ? 0 if Rmax + 1 ? < L(? st ) 2 6 with linear ramps between Rmin ? 1 ? < L(? st ) < Rmin + 1 ? and Rmax ? 1 ? < L(? st ) < Rmax + 1 ?. As 2 2 2 2 above, most banks would choose to use the ? oorlet spreads (with ? being 5bps or 10bps) instead of using the more troublesome digitals. For a bank insisting on using exact digital options, one can take ? to be 0. 5bps to replicate the digital accurately.. We now just need to sum over all days ? t in period j and all periods j in the coupon leg, (2. 15) Vcpn (t) = n X This formula replicates the value of the range note in terms of vanilla ? oorlets. These ? oorlet prices should be obtained directly from the marketplace using market quotes for the implied volatilities at the relevent strikes. Of course the centerred spreads could be replaced by super-replicating or sub-replicating ? oorlet spreads, bringing the pricing in line with the bank’s policies. Finally, we need to value the funding leg of the accrual swap. For most accrual swaps, the funding leg ? ? pays ? oating plus a margin. Let th e funding leg dates be t0 , t1 , . . , tn . Then the funding leg payments are (2. 16) f ? ? cvg(ti? 1 , ti )[Ri lt + mi ]  ¤ A(t0 , ? st )  ©? 1 + (Rmax ? 1 ? ) F (t; ? st , Rmax + 1 ? ) 2 2 j=1 ? st =tj? 1 +1 ?  ¤ ? 1 + (Rmax + 1 ? ) F (t; ? st , Rmax ? 1 ? ) 2 2 ?  ¤ ? 1 + (Rmin ? 1 ? ) F (t; ? st , Rmin + 1 ? ) 2 2 ?  ¤ ? + 1 + (Rmin + 1 ? ) F (t; ? st , Rmin ? 1 ? ) . 2 2 tj X ? paid at ti , i = 1, 2, †¦ , n, ? f ? ? where Ri lt is the ? oating rate’s ? xing for the period ti? 1 < t < ti , and the mi is the margin. The value of the funding leg is just n ? X i=1 (2. 17a) Vf und (t) = ? ? ? cvg(ti? 1 , ti )(ri + mi )Z(t; ti ), ? ? where, by de? ition, ri is the forward value of the ? oating rate for period ti? 1 < t < ti : (2. 17b) ri = ? ? Z(t; ti? 1 ) ? Z(t; ti ) true + bs0 . + bs0 = ri i i ? ? ? cvg(ti? 1 , ti )Z(t; ti ) true is the true (cash) rate. This sum Here bs0 is the basis spread for the funding leg’s ? oating rate, and ri i collapses t o n ? X i=1 (2. 18a) Vf und (t) = Z(t; t0 ) ? Z(t; tn ) + ? ? ? ? cvg(ti? 1 , ti )(bs0 +mi )Z(t; ti ). i If we include only the funding leg payments for i = i0 to n, the value is ? (2. 18b) ? Vf und (t) = Z(t; ti0 ? 1 ) ? Z(t; tn ) + ? n ? X ? ? ? cvg(ti? 1 , ti )(bs0 +mi )Z(t; ti ). i i=i0 2. 2. 1. Pricing notes. Caplet/? oorlet prices are normally quoted in terms of Black vols. Suppose that on date t, a ? oorlet with ? xing date tf ix , start date ? st , end date ? end , and strike K has an implied vol of ? imp (K) ? ? imp (? st , K). Then its market price is (2. 19a) F (t, ? st , K) = ? Z(t; ? end ) {KN (d1 ) ? L(t, ? )N (d2 )} , 7 where (2. 19b) Here (2. 19c) d1,2 = log K/L(t, ? st )  ± 1 ? 2 (K)(tf ix ? t) 2 imp , v ? imp (K) tf ix ? t Z(t; ? st ) ? Z(t; ? end ) + bs(? st ) ? Z(t; ? end ) L(t, ? st ) = is ? oorlet’s forward rate as seen at date t. Today’s ? oorlet value is simply (2. 20a) where (2. 20b) d1,2 = log K/L0 (? st )  ± 1 ? (K)tf ix 2 imp , v ? imp (K) tf ix D(? st ) ? D(? end ) + bs(? st ). ?D(? end ) ? j Rf ix D(tj ) 1 . Mj D(? end ) 1 + L0 (? st ) F (0, ? st , K) = ? D(? end ) {KN (d1 ) ? L0 (? )N (d2 )} , and where today’s forward Libor rate is (2. 20c) L0 (? st ) = To obtain today’s price of the accrual swap, note that the e? ective notional for period j is (2. 21) A(0, ? st ) = as seem today. See 2. 11b. Putting this together with 2. 13a shows that today’s price is Vcpn (0) ? Vf und (0), where (2. 22a) Vcpn (0) = n X ? j Rf ix D(tj ) j=1 Mj  ¤ ?  ¤ ? 1 + (Rmax ? 1 ? ) B1 (? st ) ? 1 + (Rmax + 1 ? ) B2 (? st ) 2 2 ? [1 + L0 (? st )] ? t =tj? 1 +1  ¤ ?  ¤ ? 1 + (Rmin ? 1 ? ) B3 (? st ) ? 1 + (Rmin + 1 ? ) B4 (? st ) 2 2 ? , ? [1 + L0 (? st )] tj X n ? X i=1 (2. 22b) Vf und (0) = D(t0 ) ? D(tn ) + ? ? ? ? cvg(ti? 1 , ti )(bs0 +mi )D(ti ). i Here B? are Black’s formula at strikes around the boundaries: (2. 22c) (2. 22d) with (2. 22e) K1,2 = Rmax  ± 1 ? , 2 K3,4 = Rmin  ± 1 ?. 2 B? (? st ) = K? N (d? ) ? L0 (? st )N (d? ) 1 2 d? = 1,2 log K? /L0 (? st )  ± 1 ? 2 (K? )tf ix 2 imp v ? imp (K? ) tf ix Calculating the sum of each day’s contribution is very tedious. Normally, one calculates each day’s contribution for the current period and two or three months afterward. After that, one usually replaces the sum over dates ? with an integral, and samples the contribution from dates ? one week apart for the next year, and one month apart for subsequent years. 8 3. Callable accrual swaps. A callable accrual swap is an accrual swap in which the party paying the coupon leg has the right to cancel on any coupon date after a lock-out period expires. For example, a 10NC3 with 5 business days notice can be called on any coupon date, starting on the third anniversary, provided the appropriate notice is given 5 days before the coupon date. We will value the accrual swap from the viewpoint of the receiver, who would price the callable accrual swap as the full accrual swap (coupon leg minus funding leg) minus the Bermudan option to enter into the receiver accrual swap. So a 10NC3 cancellable quarterly accrual swap would be priced as the 10 year bullet quarterly receiver accrual swap minus the Bermudan option – with quarterly exercise dates starting in year 3 – to receive the remainder of the coupon leg and pay the remainder of the funding leg. Accordingly, here we price Bermudan options into receiver accrual swaps. Bermudan options on payer accrual swaps can be priced similarly. There are two key requirements in pricing Bermudan accrual swaps. First, as Rmin decreases and Rmax increases, the value of the Bermudan accrual swap should reduce to the value of an ordinary Bermudan swaption with strike Rf ix . Besides the obvious theoretical appeal, meeting this requirement allows one to hedge the callability of the accrual swap by selling an o? setting Bermudan swaption. This criterion requires using the same the interest rate model and calibration method for Bermudan accrual notes as would be used for Bermudan swaptions. Following standard practice, one would calibrate the Bermudan accrual note to the â€Å"diagonal swaptions† struck at the accrual note’s â€Å"e? ective strikes. † For example, a 10NC3 accrual swap which is callable quarterly starting in year 3 would be calibrated to the 3 into 7, the 3. 25 into 6. 75, †¦ , the i 8. 75 into 1. 25, and the 9 into 1 swaptions. The strike Ref f for each of these â€Å"reference swaptions† would be chosen so that for swaption i, (3. 1) value of the ? xed leg value of all accrual swap coupons j ? i = value of the ? oating leg value of the accrual swap’s funding leg ? i This usually results in strikes Ref f that are not too far from the money. In the preceding section we showed that each coupon of the accrual swap can be written as a combination of vanilla ? oorlets, and therefore the market value of each coupon is known exactly. The second requirement is that the valuation procedure should reproduce today’s m arket value of each coupon exactly. In fact, if there is a 25% chance of exercising into the accrual swap on or before the j th exercise date, the pricing methodology should yield 25% of the vega risk of the ? oorlets that make up the j th coupon payment. E? ectively this means that the pricing methodology needs to use the correct market volatilities for ? oorlets struck at Rmin and Rmax . This is a fairly sti? requirement, since we now need to match swaptions struck at i Ref f and ? oorlets struck at Rmin and Rmax . This is why callable range notes are considered heavily skew depedent products. 3. 1. Hull-White model. Meeting these requirements would seem to require using a model that is sophisticated enough to match the ? oorlet smiles exactly, as well as the diagonal swaption volatilities. Such a model would be complex, calibration would be di? ult, and most likely the procedure would yield unstable hedges. An alternative approach is to use a much simpler model to match the diagonal swaption prices, and then use â€Å"internal adjusters† to match the ? oorlet volatilities. Here we follow this approach, using the 1 factor linear Gauss Markov (LGM) model with internal adjusters to price Bermudan options on accrual swaps. Speci ? cally, we ? nd explicit formulas for the LGM model’s prices of standard ? oorlets. This enables us to compose the accrual swap â€Å"payo? s† (the value recieved at each node in the tree if the Bermudan is exercised) as a linear combination of the vanilla ? orlets. With the payo? s known, the Bermudan can be evaluated via a standard rollback. The last step is to note that the LGM model misprices the ? oorlets that make up the accrual swap coupons, and use internal adjusters to correct this mis-pricing. Internal adjusters can be used with other models, but the mathematics is more complex. 3. 1. 1. LGM. The 1 factor LGM model is exactly the Hull-White model expressed as an HJM model. The 1 factor LGM model has a single state variable x that determines the entire yield curve at any time t. 9 This model can be summarized in three equations. The ? st is the Martingale valuation formula: At any date t and state x, the value of any deal is given by the formula, Z V (t, x) V (T, X) (3. 2a) = p(t, x; T, X) dX for any T > t. N (t, x) N (T, X) Here p(t, x; T, X) is the probability that the state variable is in state X at date T , given that it is in state x at date t. For the LGM model, the transition density is Gaussian 2 1 e? (X? x) /2[? (T ) (t)] , p(t, x; T, X) = p 2? [? (T ) ? ?(t)] (3. 2b) with a variance of ? (T ) ? ?(t). The numeraire is (3. 2c) N (t, x) = 1 h(t)x+ 1 h2 (t)? (t) 2 , e D(t) for reasons that will soon become apparent. Without loss of generality, one sets x = 0 at t = 0, and today’s variance is zero: ? (0) = 0. The ratio (3. 3a) V (t, x) ? V (t, x) ? N (t, x) is usually called the reduced value of the deal. Since N (0, 0) = 1, today’s value coincides with today’s reduced value: (3. 3b) V (0, 0) ? V (0, 0) = V (0, 0) ? . N (0, 0) So we only have to work with reduced values to get today’s prices.. De? ne Z(t, x; T ) to be the value of a zero coupon bond with maturity T , as seen at t, x. It’s value can be found by substituting 1 for V (T, X) in the Martingale valuation formula. This yields (3. 4a) 1 2 Z(t, x; T ) ? Z(t, x; T ) ? = D(T )e? (T )x? 2 h (T )? (t) . N (t, x) Since the forward rates are de? ned through (3. 4b) Z(t, x; T ) ? e? T t f (t,x;T 0 )dT 0 , ? taking ? ?T log Z shows that the forward rates are (3. 4c) f (t, x; T ) = f0 (T ) + h0 (T )x + h0 (T )h(T )? (t). This last equation captures the LGM model in a nutshell. The curves h(T ) and ? (t) are model parameters that need to be set by calibration or by a priori reasoning. The above formula shows that at any date t, the forward rate curve is given by today’s forward rate curve f0 (T ) plus x times a second curve h0 (T ), where x is a Gaussian random variable with mean zero and variance ? (t). Thus h0 (T ) determines possible shapes of the forward curve and ? (t) determines the width of the distribution of forward curves. The last term h0 (T )h(T )? (t) is a much smaller convexity correction. 10 3. 1. 2. Vanilla prices under LGM. Let L(t, x; ? st ) be the forward value of the k month Libor rate for the period ? st to ? end , as seen at t, x. Regardless of model, the forward value of the Libor rate is given by (3. 5a) where (3. 5b) ? = cvg(? st , ? end ) L(t, x; ? st ) = Z(t, x; ? st ) ? Z(t, x; ? end ) + bs(? st ) = Ltrue (t, x; ? st ) + bs(? st ), ? Z(t, x; ? end ) is the day count fraction of the interval. Here Ltrue is the forward â€Å"true rate† for the interval and bs(? ) is the Libor rate’s basis spread for the period starting at ? . Let F (t, x; ? st , K) be the value at t, x of a ? oorlet with strike K on the Libor rate L(t, x; ? st ). On the ? xing date ? f ix the payo? is (3. 6) ?  ¤+ F (? f ix , xf ix ; ? st , K) = ? K ? L(? f ix , xf ix ; ? st ) Z(? f ix , xf ix ; ? end ), where xf ix is the state variable on the ? xing date. Substituting for L(? ex , xex ; ? st ), the payo? becomes (3. 7a)  · ? + F (? f ix , xf ix ; ? st , K) Z(? f ix , xf ix ; ? st ) Z(? f ix , xf ix ; ? end ) . = 1 + ? (K ? bs(? st )) ? N (? ix , xf ix ) N (? f ix , xf ix ) Z(? f ix , xf ix ; ? end ) Knowing the value of the ? oorlet on the ? xing date, we can use the Martingale valuation formula to ? nd the value on any earlier date t: Z 2 1 F (t, x; ? st , K) F (? f ix , xf ix ; ? st , K) e? (xf ix ? x) /2[? f ix ] =q dxf ix , (3. 7b) N (t, x) N (? f ix , xf ix ) 2? [? f ix ? ?] where ? f ix = ? (? f ix ) and ? = ? (t). Substituting the zero coupon bond formula 3. 4a and the payo? 3. 7a into the integral yields (3. 8a) where log (3. 8b) ? 1,2 =  µ 1 + ? (K ? bs) 1 + ? (L ? bs)  ¤ ?  ± 1 (hend ? hst )2 ? f ix ? ?(t) 2 q , (hend ? hst ) ? f ix ? (t)  ¶ F (t, x; ? st , K) = Z(t, x; ? end ) {[1 + ? (K ? bs)]N (? 1 ) ? [1 + ? (L ? bs)]N (? 2 )} , and where L ? L(t, x; ? st ) = (3. 8c)  µ  ¶ 1 Z(t, x; ? st ) ? 1 + bs(? st ) ? Z(t, x; ? end )  ¶  µ 1 Dst (hend ? hst )x? 1 (h2 ? h2 )? end st 2 = e ? 1 + bs(? st ) ? Dend 11 is the forward Libor rate for the period ? st to ? end , as seen at t, x. Here hst = h(? st ) and hend = h(? end ). For future reference, it is convenient to split o? the zero coupon bond value Z(t, x; ? end ). So de? ne the forwarded ? oorlet value by (3. 9) Ff (t, x; ? st , K) = F (t, x; ? st , K) Z(t, x; ? end ) = [1 + ? (K ? bs)]N (? 1 ) ? [1 + ? L(t, x; ? st ) ? bs)]N (? 2 ). Equations 3. 8a and 3. 9 are just Black’s formul as for the value of a European put option on a log normal asset, provided we identify (3. 10a) (3. 10b) (3. 10c) (3. 10d) 1 + ? (L ? bs) = asset’s forward value, 1 + ? (K ? bs) = strike, ? end = settlement date, and p ? f ix ? ? (hend ? hst ) v = ? = asset volatility, tf ix ? t where tf ix ? t is the time-to-exercise. One should not confuse ? , which is the ? oorlet’s â€Å"price volatility,† with the commonly quoted â€Å"rate volatility. † 3. 1. 3. Rollback. Obtaining the value of the Bermudan is straightforward, given the explicit formulas for the ? orlets, . Suppose that the LGM model has been calibrated, so the â€Å"model parameters† h(t) and ? (t) are known. (In Appendix A we show one popular calibration method). Let the Bermudan’s noti? cation dates be tex , tex+1 , . . . , tex . Suppose that if we exercise on date tex , we receive all coupon payments for the K k0 k0 k intervals k + 1, . . . , n and recieve all funding leg payments f or intervals ik , ik + 1, . . . , n. ? The rollback works by induction. Assume that in the previous rollback steps, we have calculated the reduced value (3. 11a) V + (tex , x) k = value at tex of all remaining exercises tex , tex . . . , tex k k+1 k+2 K N (tex , x) k at each x. We show how to take one more step backwards, ? nding the value which includes the exercise tex k at the preceding exercise date: (3. 11b) V + (tex , x) k? 1 = value at tex of all remaining exercises tex , tex , tex . . . . , tex . k? 1 k k+1 k+2 K N (tex , x) k? 1 Let Pk (x)/N (tex , x) be the (reduced) value of the payo? obtained if the Bermudan is exercised at tex . k k As seen at the exercise date tex the e? ective notional for date ? st is k (3. 12a) where we recall that (3. 12b) ? = ? end (? st ) ? tj , ? end (? st ) ? ? st ? = cvg(? st , ? end (? st )). 12 A(tex , x, ? t ) = k ?j Rf ix Z(tex , x; tj ) 1 k , Mj Z(tex , x; ? end ) 1 + Lf (tex , x; ? st ) k k Reconstructing the reduced value of the payo? (see equation 2. 15) yields (3. 13a) Pk (x) = N (tex , x) k n X ? j Rf ix Z(tex , x; tj ) k Mj N (tex , x) ? k tj X j=k+1 st =tj? 1 +1 ? 1 + (Rmax ? 1 ? ) 2 Ff (tex , x; ? st , Rmax + 1 ? ) k 2 1 + Lf (tex , x; ? st ) k ? ? 1 + (Rmax + 1 ? ) 2 Ff (tex , x; ? st , Rmax ? 1 ? ) k 2 1 + Lf (tex , x; ? st ) k 1 + (Rmin ? 1 ? ) 2 Ff (tex , x; ? st , Rmin + 1 ? ) k 2 1 + Lf (tex , x; ? st ) k 1 + (Rmin + 1 ? ) 2 + Ff (tex , x; ? st , Rmin ? 1 ? ) k 2 1 + Lf (tex , x; ? st ) k ? n ? X ? ? Z(tex , x, tik ? 1 ) ? Z(tex , x, tn ) Z(tex , x, ti ) k k k ? ? cvg(ti? 1 , ti )(bsi +mi ) ? ex , x) ex , x) . N (tk N (tk i=i +1 k ? This payo? includes only zero coupon bonds and ? oorlets, so we can calculate this reduced payo? explicitly using the previously derived formula 3. 9. The reduced valued including the kth exercise is clearly ? ? Pk (x) V + (tex , x) V (tex , x) k k = max , at each x. (3. 13b) N (tex , x) N (tex , x) N (tex , x) k k k Using the Martingale valuation formula we can â€Å"roll di? erences, trees, convolution, or direct integration to Z V + (tex , x) 1 k? 1 (3. 3c) =p N (tex , x) 2? [? k ? ? k? 1 ] k? 1 back† to the preceding exercise date by using ? nite compute the integral V (tex , X) ? (X? x)2 /2[? k k? 1 ] k dX e N (tex , X) k at each x. Here ? k = ? (tex ) and ? k? 1 = ? (tex ). k k? 1 At this point we have moved from tex to the preceding exercise date tex . We now repeat the procedure: k k? 1 at each x we t ake the max of V + (tex , x)/N (tex , x) and the payo? Pk? 1 (x)/N (tex , x) for tex , and then k? 1 k? 1 k? 1 k? 1 use the valuation formula to roll-back to the preceding exercise date tex , etc. Eventually we work our way k? 2 througn the ? rst exercise V (tex , x). Then today’s value is found by a ? nal integration: k0 Z V (tex , X) ? X 2 /2? V (0, 0) 1 k0 k0 dX. (3. 14) V (0, 0) = =p e N (0, 0) N (tex , X) 2 k0 k0 3. 2. Using internal adjusters. The above pricing methodology satis? es the ? rst criterion: Provided we use LGM (Hull-White) to price our Bermudan swaptions, and provided we use the same calibration method for accrual swaps as for Bermudan swaptions, the above procedure will yield prices that reduce to the Bermudan prices as Rmin goes to zero and Rmax becomes large. However the LGM model yields the following formulas for today’s values of the standard ? orlets: F (0, 0; ? st , K) = D(? end ) {[1 + ? (K ? bs)]N (? 1 ) ? [1 + ? (L0 ? bs)]N (? 2 )} log  µ  ¶ 1 + ? (K ? bs)  ± 1 ? 2 tf ix 2 mod 1 + ? (L0 ? bs) . v ? mod tf ix 13 (3. 15a) where (3. 15b) ?1,2 = Here (3. 15c) L0 = Dst ? Dend + bs(? st ) ? Dend is today’s forward value for the Libor rate, and (3. 15d) q ? mod = (hend ? hst ) ? f ix /tf ix 3. 2. 1. Obtaining the market vol. Floorlets are quoted in terms of the ordinary (rate) vol. Suppose the rate vol is quoted as ? imp (K). Then today’s market price of the ? oorlet is is the asset’s log normal volatility according to the LGM model. We did not calibrate the LGM model to these ? oorlets. It is virtually certain that matching today’s market prices for the ? oorlets will require using q an implied (price) volatility ? mkt which di? ers from ? mod = (hend ? hst ) ? f ix /tf ix . (3. 16a) where (3. 16b) Fmkt (? st , K) = ? D(? end ) {KN (d1 ) ? L0 N (d2 )} d1,2 = log K/L0  ± 1 ? 2 (K)tf ix 2 imp v ? imp (K) tf ix The price vol ? mkt is the volatility that equates the LGM ? oorlet value to this market value. It is de? ned implicitly by (3. 17a) with log (3. 17b) ? 1,2 =  µ  ¶ 1 + ? (K ? bs)  ± 1 ? 2 tf ix 2 mkt 1 + ? (L0 ? bs) v ? kt tf ix [1 + ? (K ? bs)]N (? 1 ) ? [1 + ? (L0 ? bs)]N (? 2 ) = ? KN (d1 ) ? ?L0 N (d2 ), (3. 17c) d1,2 = log K/L0  ± 1 ? 2 (K)tf ix 2 imp v ? imp (K) tf ix Equivalent vol techniques can be used to ? nd the price vol ? mkt (K) which corresponds to the market-quoted implied rate vol ? imp (K) : (3. 18) ? imp (K) = 1 + 5760 ? 4 t2 ix +  ·  ·  · 1+ imp f ? mkt (K) 1 2 1 4 2 24 ? mkt tf ix + 5760 ? mkt tf ix  µ log L0 /K  ¶ 1 + ? (L0 ? bs) 1 + ? (K ? bs) 1+ 1 2 24 ? imp tf ix log If this approximation is not su? ciently accurate, we can use a single Newton step to attain any reasonable accuracy. 14 igital floorlet value ? mod ? mkt L0/K Fig. 3. 1. Unadjusted and adjusted digital payo? L/K 3. 2. 2. Adjusting the price vol. The price vol ? mkt obtained from the market price will not match the q LGM model’s price vol ? mod = (hend ? hst ) ? f ix /tf ix . This is easily remedied using an internal adjuster. All one does is multiply the model volatility with the factor needed to bring it into line with the actual market volatility, and use this factor when calculating the payo? s. Speci? cally, in calculating each payo? Pk (x)/N (tex , x) in the rollback (see eq. 3. 13a), one makes the replacement k (3. 9) (3. 20) (hend ? hst ) q q ? mkt ? f ix ? ?(tex ) =? (hend ? hst ) ? f ix ? ?(t) k ? mod q p = 1 ? ?(tex )/? (tf ix )? mkt tf ix . k With the internal adjusters, the pricing methodology now satis? es the second criteria: it agrees with all the vanilla prices that make up the range note coupons. Essentially, all the adjuster does is to slightly â€Å"sharpen up† or â€Å"smear out† the digital ? oorlet’s payo? to match today’s value at L0 /K. This results in slightly positive or negative price corrections at various values of L/K, but these corrections average out to zero when averaged over all L/K. Making this volatility adjustment is vastly superior to the other commonly used adjustment method, which is to add in a ? ctitious â€Å"exercise fee† to match today’s coupon value. Adding a fee gives a positive or negative bias to the payo? for all L/K, even far from the money, where the payo? was certain to have been correct. Meeting the second criterion forced us to go outside the model. It is possible that there is a subtle arbitrage to our pricing methodology. (There may or may not be an arbitrage free model in which extra factors – positively or negatively correlated with x – enable us to obtain exactly these ? orlet prices while leaving our Gaussian rollback una? ected). However, not matching today’s price of the underlying accrual swap would be a direct and immediate arbitrage. 15 4. Range notes and callable range notes. In an accrual swap, the coupon leg is exchanged for a funding leg, which is normally a standard Libor leg plus a margin. U nlike a bond, there is no principle at risk. The only credit risk is for the di? erence in value between the coupon leg and the ? oating leg payments; even this di? erence is usually collateralized through various inter-dealer arrangements. Since swaps are indivisible, liquidity is not an issue: they can be unwound by transferring a payment of the accrual swap’s mark-to-market value. For these reasons, there is no detectable OAS in pricing accrual swaps. A range note is an actual bond which pays the coupon leg on top of the principle repayments; there is no funding leg. For these deals, the issuer’s credit-worthiness is a key concern. One needs to use an option adjusted spread (OAS) to obtain the extra discounting re? ecting the counterparty’s credit spread and liquidity. Here we analyze bullet range notes, both uncallable and callable. The coupons Cj of these notes are set by the number of days an index (usually Libor) sets in a speci? ed range, just like accrual swaps: ? tj X ? j Rf ix 1 if Rmin ? L(? st ) ? Rmax (4. 1a) Cj = , 0 otherwise Mj ? =t +1 st j? 1 where L(? st ) is k month Libor for the interval ? st to ? end (? st ), and where ? j and Mj are the day count fraction and the total number of days in the j th coupon interval tj? 1 to tj . In addition, these range notes repay the principle on the ? nal pay date, so the (bullet) range note payments are: (4. 1b) (4. 1c) Cj 1 + Cn paid on tj , paid on tn . j = 1, 2, . . . n ? 1, For callable range notes, let the noti? ation on dates be tex for k = k0 , k0 + 1, . . . , K ? 1, K with K < n. k Assume that if the range note is called on tex , then the strike price Kk is paid on coupon date tk and the k payments Cj are cancelled for j = k + 1, . . . , n. 4. 1. Modeling option adjusted spreads. Suppose a range note is issued by issuer A. ZA (t, x; T ) to be the value of a dollar paid by the note on date T , as seen at t, x. We assume that (4. 2) ZA (t, x; T ) = Z(t, x; T ) ? (T ) , ? (t) De? ne where Z(t, x; T ) is the value according to the Libor curve, and (4. 3) ? (? ) = DA (? ) . e D(? ) Here ? is the OAS of the range note. The choice of the discount curve DA (? ) depends on what we wish the OAS to measure. If one wishes to ? nd the range note’s value relative to the issuer’s other bonds, then one should use the issuer’s discount curve for DA (? ); the OAS then measures the note’s richness or cheapness compared to the other bonds of issuer A. If one wishes to ? nd the note’s value relative to its credit risk, then the OAS calculation should use the issuer’s â€Å"risky discount curve† or for the issuer’s credit rating’s risky discount curve for DA (? ). If one wishes to ? nd the absolute OAS, then one should use the swap market’s discount curve D(? , so that ? (? ) is just e . When valuing a non-callable range note, we are just determining which OAS ? is needed to match the current price. I. e. , the OAS needed to match the market’s idiosyncratic preference or adversion of the bond. When valuing a callable range note, we are ma king a much more powerful assumption. By assuming that the same ? can be used in evaluating the calls, we are assuming that (1) the issuer would re-issue the bonds if it could do so more cheaply, and (2) on each exercise date in the future, the issuer could issue debt at the same OAS that prevails on today’s bond. 16 4. 2. Non-callable range notes. Range note coupons are ? xed by Libor settings and other issuerindependent criteria. Thus the value of a range note is obtained by leaving the coupon calculations alone, and replacing the coupon’s discount factors D(tj ) with the bond-appropriate DA (tj )e tj : (4. 4a) VA (0) = n X j=1 ?j Rf ix DA (tj )e tj Mj  ¤ ?  ¤ ? 1 + (Rmax ? 1 ? ) B1 (? st ) ? 1 + (Rmax + 1 ? ) B2 (? st ) 2 2 ? [1 + L0 (? st )] ? st =tj? 1 +1  ¤ ?  ¤ ? 1 + (Rmin ? 1 ? ) B3 (? st ) ? 1 + (Rmin + 1 ? ) B4 (? st ) 2 2 ? ? [1 + L0 (? st )] +DA (tn )e tn . tj X Here the last term DA (tn )e n is the value of the notional repaid at maturity. As before, the B? are Black’s formulas, (4. 4b) B? (? st ) = Kj N (d? ) ? L0 (? st )N (d? ) 1 2 (4. 4c) d? = 1,2 log K? /L0 (? st )  ± 1 ? 2 (K? )tf ix 2 imp v ? imp (K? ) tf ix (4. 4d) K1,2 = Rmax  ± 1 ? , 2 K3,4 = Rmin  ± 1 ? , 2 and L0 (? ) is today’s forward rate: (4. 4e) Finally, (4. 4f) ? = ? end ? tj . ? en d ? ? st L0 (? st ) = D(? st ) ? D(? end ) ? D(? end ) 4. 3. Callable range notes. We price the callable range notes via the same Hull-White model as used to price the cancelable accrual swap. We just need to adjust the coupon discounting in the payo? function. Clearly the value of the callable range note is the value of the non-callable range note minus the value of the call: (4. 5) callable bullet Berm VA (0) = VA (0) ? VA (0). bullet Berm (0) is the today’s value of the non-callable range note in 4. 4a, and VA (0) is today’s value of Here VA the Bermudan option. This Bermudan option is valued using exactly the same rollback procedure as before, 17 except that now the payo? is (4. 6a) (4. 6b) Pk (x) = N (tex , x) k ? tj X st =tj? 1 +1 j=k+1 n X ? j Rf ix ZA (tex , x; tj ) k Mj N (tex , x) ? k 1 + (Rmax ? 1 ? ) 2 Ff (tex , x; ? st , Rmax + 1 ? ) k 2 1 + Lf (tex , x; ? st ) k ? ? + (Rmax + 1 ? ) 2 Ff (tex , x; ? st , Rmax ? 1 ? ) k 2 1 + Lf (tex , x; ? st ) k 1 + (Rmin ? 1 ? ) 2 Ff (tex , x; ? st , Rmin + 1 ? ) k 2 1 + Lf (tex , x; ? st ) k 1 + (Rmin + 1 ? ) 2 + Ff (tex , x; ? st , Rmin ? 1 ? ) k 2 1 + Lf (tex , x; ? st ) k ZA (tex , x, tn ) ZA (tex , x, tk ) k k + ? Kk ex , x) N (tk N (tex , x) k Here the bond speci? c reduced zero coupon bond value is (4. 6c) ex ex 1 2 ZA (tex , x, T ) D(tex ) k k = DA (T )e (T ? tk ) e? h(T )x? 2 h (T )? k , ex , x) N (tk DA (tex ) k ? the (adjusted) forwarded ? oorlet value is Ff (tex , x; ? st , K) = [1 + ? (K ? bs)]N (? 1 ) ? [1 + ? (L(tex , x; ? t ) ? bs)]N (? 2 ) k k log (4. 6d) ? 1,2 =  µ  ¶ 1 + ? (K ? bs)  ± 1 [1 ? ?(tex )/? (tf ix )]? 2 tf ix k mkt 2 1 + ? (L ? bs) p , v 1 ? ?(tex )/? (tf ix )? mkt tf ix k  ¶ Z(tex , x; ? st ) k ? 1 + bs(? st ) Z(tex , x; ? end ) k  ¶ (hend ? hst )x? 1 (h2 ? h2 )? ex end st k ? 1 + bs(? 2 e st ) 1 = ?  µ and the forward Libor value is (4. 6e) (4. 6f) L? L (tex , x; ? st ) k  µ Dst Dend 1 = ? The only remaining issue is calibration. For range notes, we should use constant mean reversion and calibrate along the diagonal, exactly as we did for the cancelable accrual swaps. We only need to specify the strikes of the reference swaptions. A good method is to transfer the basis spreads and margin to the coupon leg, and then match the ratio of the coupon leg to the ? oating leg. For exercise on date tk , this ratio yields (4. 7a) n X ?k = ? j Rf ix DA (tj )e (tj ? tk ) Mj Kk DA (tk ) j=k+1 (?  ¤ ?  ¤ 1 + (Rmax ? 1 ? ) B1 (? st ) ? 1 + (Rmax + 1 ? ) B1 (? st ) 2 2 ? [1 + L0 (? st )] ? st =tj? 1 +1 )  ¤ ?  ¤ ? 1 + (Rmin ? 1 ? ) B3 (? st ) ? 1 + (Rmin + 1 ? ) B3 (? st ) 2 2 ? 1 + Lf (tex , x; ? st ) k tj X + DA (tn )e (tn ? tk ) Kk DA (tk ) 18 As before, the Bj are dimensionless Black formulas, (4. 7b) B? (? st ) = K? N (d? ) ? L0 (? st )N (d? ) 1 2 d? = 1,2 log K? /L0 (? st )  ± 1 ? 2 (K? )tf ix 2 imp v ? imp (K? ) tf ix K3,4 = Rmin  ± 1 ? , 2 (4. 7c) (4. 7d) K1,2 = Rmax  ± 1 ? , 2 and L0 (? st ) is today’s forward rate: Appendix A. Calibrating the LGM model. The are several methods of calibrating the LGM model for pricing a Bermudan swaption. The most popular method is to choose a constant mean reversion ? , and then calibrate on the diagonal European swaptions making up the Bermudan. In the LGM model, a â€Å"constant mean reversion ? † means that the model function h(t) is given by (A. 1) h(t) = 1 ? e t . ? Usually the value of ? s selected from a table of values that are known to yield the correct market prices of liquid Bermudans; It is known empirically that the needed mean reversion parameters are very, very stable, changing little from year to year. ? 1M 3M 6M 1Y 3Y 5Y 7Y 10Y 1Y -1. 00% -0. 75% -0. 50% 0. 00% 0. 25% 0. 50% 1. 00% 1. 50% 2Y -0. 50% -0. 25% 0. 00% 0. 25% 0. 50% 1. 00% 1. 25% 1. 50% 3Y -0. 25% 0. 00% 0. 25% 0. 50% 1. 00% 1. 25% 1. 50% 1. 75% 4Y -0. 25% 0. 00% 0. 25% 0. 50% 1. 00% 1. 25% 1. 50% 1. 75% 5Y -0. 25% 0. 00% 0. 25% 0. 50% 1. 00% 1. 25% 1. 50% 1. 75% 7Y -0. 25% 0. 00% 0. 25% 0. 50% 1. 00% 1. 25% 1. 50% 1. 75% 10Y -0. 25% 0. 0% 0. 25% 0. 50% 1. 00% 1. 25% 1. 50% 1. 75% Table A. 1 Mean reverssion ? for Bermudan swaptions. Rows are time-to-? rst exercise; columns are tenor of the longest underlying swap obtained upon exercise. With h(t) known, we only need determine ? (t) by calibrating to European swaptions. Consider a European swaption with noti? cation date tex . Suppose that if one exercises the option, one recieves a ? xed leg worth (A. 2a) Vf ix (t, x) = n X i=1 Rf ix cvg(ti? 1 , ti , dcbf ix )Z(t, x; ti ), and pays a ? oating leg worth (A. 2b) Vf lt (t, x) = Z(t, x; t0 ) ? Z(t, x; tn ) + n X i=1 cvg(ti? 1 , ti , dcbf lt ) bsi Z(t, x; ti ). 9 Here cvg(ti? 1 , ti , dcbf ix ) and cvg(ti? 1 , ti , dcbf lt ) are the day count fraction s for interval i using the ? xed leg and ? oating leg day count bases. (For simplicity, we are cheating slightly by applying the ? oating leg’s basis spread at the frequency of the ? xed leg. Mea culpa). Adjusting the basis spread for the di? erence in the day count bases (A. 3) bsnew = i cvg(ti? 1 , ti , dcbf lt ) bsi cvg(ti? 1 , ti , dcbf ix ) allows us to write the value of the swap as (A. 4) Vswap (t, x) = Vf ix (t, x) ? Vf lt (t, x) n X = (Rf ix ? bsi ) cvg(ti? 1 , ti , dcbf ix )Z(t, x; ti ) + Z(t, x; tn ) ? Z(t, x; t0 ) i=1 Under the LGM model, today’s value of the swaption is (A. 5) 1 Vswptn (0, 0) = p 2 (tex ) Z e? xex /2? (tex ) 2 [Vswap (tex , xex )]+ dxex N (tex , xex ) Substituting the explicit formulas for the zero coupon bonds and working out the integral yields (A. 6a) n X (Rf ix ? bsi ) cvg(ti? 1 , ti , dcbf ix )D(ti )N Vswptn (0, 0) = where y is determined implicitly via (A. 6b) y + [h(ti ) ? h(t0 )] ? ex p ? ex i=1 A A ! ! y + [h(tn ) ? h(t0 )] ? ex y p ? D(t0 )N p , +D(tn )N ? ex ? ex A ! n X 2 1 (Rf ix ? bsi ) cvg(ti? 1 , ti , dcbf ix )e? [h(ti )? h(t0 )]y? 2 [h(ti )? h(t0 )] ? ex i=1 +D(tn )e? [h(tn )? h(t0 )]y? [h(tn )? h(t0 )] 1 2 ? ex = D(t0 ). The values of h(t) are known for all t, so the only unknown parameter in this price is ? (tex ). One can show that the value of the swaption is an increasing function of ? (tex ), so there is exactly one ? (tex ) which matches the LGM value of the swaption to its market price. This solution is easily found via a global Newton iteration. T o price a Bermudan swaption, one typcially calibrates on the component Europeans. For, say, a 10NC3 Bermudan swaption struck at 8. 2% and callable quarterly, one would calibrate to the 3 into 7 swaption struck at 8. 2%, the 3. 25 into 6. 5 swaption struck at 8. 2%, †¦ , then 8. 75 into 1. 25 swaption struck at 8. 25%, and ? nally the 9 into 1 swaption struck at 8. 2%. Calibrating each swaption gives the value of ? (t) on the swaption’s exercise date. One generally uses piecewise linear interpolation to obtain ? (t) at dates between the exercise dates. The remaining problem is to pick the strike of the reference swaptions. A good method is to transfer the basis spreads and margin to the coupon leg, and then match the ratio of the coupon leg to the funding leg to the equivalent ratio for a swaption. For the exercise on date tk , this ratio is de? ed to be 20 n X ? j D(tj ) (A. 7a) ? k = Mj D(tk ) ? j=k+1 D(tn ) X D(ti ) + cvg(ti? 1 , ti )(bs0 +mi ) ? i D(tk ) i=1 D(tk ) n  ¤ ?  ¤ 1 + (Rmax ? 1 ? ) B1 (? st ) ? 1 + (Rmax + 1 ? ) B2 (? st ) 2 2 ? [1 + L0 (? st )] st =tj? 1 +1  ¤ ?  ¤ ? 1 + (Rmin ? 1 ? ) B3 (? st ) ? 1 + (Rmin + 1 ? ) B4 (? st ) 2 2 ? ? [1 + L0 (? st )] tj X ? where B? are Black’s formula at strikes around the boundaries: (A. 7b) B? (? st ) = ? D(? end ) {K? N (d? ) ? L0 (? st )N (d? )} 1 2 d? = 1,2 log K? /L0 (? st )  ± 1 ? 2 (K? )tf ix 2 imp v ? imp (K? ) tf ix (A. 7c) with (A. 7d) K1,2 = Rmax  ± 1 ? , 2 K3,4 = Rmin  ± 1 ?. 2 This is to be matched to the swaption whose swap starts on tk and ends on tn , with the strike Rf ix chosen so that the equivalent ratio matches the ? k de? ned above: (A. 7e) ? k = n X i=k+1 (Rf ix ? bsi ) cvg(ti? 1 , ti , dcbf ix ) D(ti ) D(tn ) + D(tk ) D(tk ) The above methodology works well for deals that are similar to bullet swaptions. For some exotics, such as amortizing deals or zero coupon callables, one may wish to choose both the tenor of the and the strike of the reference swaptions. This allows one to match the exotic deal’s duration as well as its moneyness. Appendix B. Floating rate accrual notes. 21

Dickens novels Essay

Hard Times was one of Dickens’ novels that focuses mainly on the education system and industrialisation. Dickens was furious about the changes in industrialisation throughout the Victorian period and this motivated him enormously to write the novel. Industrialisation meant that working conditions were poor and it had a massive impact on the way schools were run. Dickens hated Victorian schools; he saw the Victorian education system as boring and monotonous and often wrote essays to show his anger and frustration at the government and those responsible for what he saw as the poor schooling techniques. Dickens creates Coketown in this novel and it is used as a representation of the government at that time and is seen as a perfect world for the fact obsessed characters but the novel explores how this way of living is not healthy. Dickens suggests that facts have become a way of life, like a religion, which was very unacceptable for that time because in the Victorian period people were especially religious and that facts were taking over a religion would have been seen as disgusting  Dickens suggests that English towns around the industrialized era are ugly, polluted and debilitated, he suggests this because facts, repetition and the lack of individuality was taking over, one of the ways he achieves this is through his description of coketown. ‘Coketown’ suggests a very scary, dull and boring place, Dickens would have intended us to have this perception because this is how he saw the government’s way of teaching and he wanted us to perceive it in the same way that he did. He also wanted us to see through his description how monotonous and unhealthy the town and way of life in that area had become. Dickens describes the school in this novel as bland, containing no creativeness, or embellishment, a framework built purely on facts and reality alone. The rooms consist of white-washed walls, stripped and bare revealing the actuality industry at the time. Dickens describes the rooms as ‘plain, bare monotonous vault of a school-room’. The word ‘vault’ suggests the school-room takes the image of a jail cell; bare, isolated, barred windows. Therefore this also suggests the pupils attending the school represent prisoners- influenced by the oppressive rules and watchful eye of Gradgrind. Their order is even arranged like prisoners, in a regular pattern, rows spaced evenly, closely monitored and not allowed to move.The rooms consist of white-washed walls, stript and bare revealing the actuality industry at the time. Dickens describes the rooms as ‘plain, bare monotonous vault of a school One of the main statements Dickens is trying to make throughout this novel is the obsession and repetitiveness of facts. The word fact is repeated so much that it feels like its being shoved into the children’s heads. â€Å"We hope to have, before long, a board of fact, composed of commissioners of fact, who will force the people to be a people of fact and nothing but fact.† This firstly shows that it is not just Gradgrind that is obsessed with facts, it is the whole school; implying the whole education system is like this. Also they wish for the facts to be ‘forced’ upon all people as they are doing in the school. Dickens put Gradgrind across as forceful, having high standards, obsessed and full of facts and wishing every one of his pupils to be as smart as he is. Mr M’Choakumchild is portrayed very similarly to Gradgrind, this gives the impression that all teachers of this time were like this. A character who is a representation for Dickens views is Gradgrind. He is used as a representation because he is made to be everything Dickens is against where education is concerned. ‘Forming the minds of reasoning animals’, Gradgrind is referring to the children as animals for testing out his way of education, he does not see them as human he sees them as animals that he needs to train to be just like him. However there are characters in the novel that challenge his way of teaching and try to be individual but Gradgrind sees this as wrong and tries to stop them and get them back in line. actuality industry at the time. Dickens describes the rooms as ‘plain, bare monotonous vault of a school-room’. The word ‘vault’ suggests the school-room takes the image of a jail cell; bare, isolated, barred windows. Therefore this also suggests the pupils attending the schooactuality industry at the time. Dickens describes the rooms as ‘plain, bare monotonous vault of a school-room’. The word ‘vault’ suggests the school-room takes the image of a jail cell; bare, isolated, barred windows. Therefore this also suggests the pupils attending the school represent prisoners- influenced by the oppressive rules and watchful eye of Gradgrind. Their order is even arranged like prisoners, in a regular pattern, rows spaced evenly, closely monitored and not allowed to move.One character who shows a contrast to the Victorian education system is Sissy Jupe. She is polite and full of life, she curtsy’s to address to Gradgrind and this shows how cheerful and polite she is. You can tell sissy loves and respects her father a lot from when she says ‘it’s father calls me Sissy sir’. Gradgrind tries to intimidate Sissy and because she is such a shy character Gradgrind easily embarrasses her with his intimidation ‘she would have blushed deeper, is she could have blushed deeper†¦Ã¢â‚¬â„¢ This shows the healthy colour in her face which represents how full of life she is and the fact she could have blushed deeper and deeper shows that she has so many different ideas and wonderful individuality that they just want to burst out of her as she is being made to keep them locked inside her.

Definition and Discussion of the Minutes of a Meeting

Definition and Discussion of the Minutes of a Meeting In business writing, minutes are the official written record of a meeting. Minutes serve as a permanent record of  the topics considered, conclusions reached, actions taken, and assignments given.   Minutes may be kept by any individual in attendance at a meeting and are usually distributed to all members of the unit represented at the meeting.Minutes are generally written in the simple past tense. The Main Parts of Meeting Minutes Many organizations use a standard template or a special format for keeping minutes, and the order of the parts may vary. HeadingThe name of the committee (or other unit) and the date, location, and starting time of the meeting.ParticipantsThe name of the person conducting the meeting along with the names of all those who attended the meeting (including guests) and those who were excused from attending.Approval of previous minutesA note on whether the minutes of the previous meeting were approved and whether any corrections were made.Action items (including unfinished business from the previous meeting)A report on each topic discussed at the meeting. (For each item, note the subject of the discussion, the name of the person who led the discussion, and any decisions that may have been reached.)AnnouncementsA report on any announcements made by participants, including proposed agenda items for the next meeting.Next MeetingA note on where and when the next meeting will be held.AdjournmentA note on the time the meeting ended.Signature lineThe name of the person who prepared the minutes and the date they wer e submitted. Observations A good set of minutes  can give the group a sense of progress; incoherent jottings (which may more closely resemble verbatim transcripts) leave everyone bewildered.(David R. Buchanan, An Ethic for Health Promotion: Rethinking the Sources of Human Well-Being. Oxford University Press,  2000)In writing minutes, be clear, comprehensive, objective, and diplomatic. Do not interpret what happened; simply report it. Because meetings rarely follow the agenda perfectly, you might find it challenging to provide an accurate record of the meeting. If necessary, interrupt the discussion to request clarification.Do not record emotional exchanges between participants. Because minutes are the official record of the meeting, you want them to reflect positively on the participants and the organization.(Mike Markel, Technical Communication, 9th ed. Bedford/St. Martins, 2010)Guidelines for Writing Meeting Minutes- The recorder should be able to write the minutes in near final form as the meeting prog resses.- The minutes should focus on results and agreed-on actions. . . .- The minutes should be highly summarized, not a burden to read. Be brief; summarize outcomes and points of agreement and disagreement; dont record detailed input.- Avoid writing minutes for the purpose of informing those absent from the meeting.- Write the minutes soon after the meeting and distribute them promptly (within a day or two).(Murray Hiebert and Bruce Klatt, The Encyclopedia of Leadership: A Practical Guide to Popular Leadership. McGraw-Hill, 2001) The Lighter Side of Minutes Russell Stringer  Bell:  [W]hat is that?Sean Shamrock  McGinty: Robert Rules say we gotta have minutes for a meeting, right? These the minutes.Russell Stringer Bell:  [I]s you taking notes on a criminal . . . conspiracy?(Idris Elba and Richard Burton in Straight and True. The Wire, 2004)

The relationship that Heaney writes about between himself and his father Essay Example

The relationship that Heaney writes about between himself and his father Essay Example The relationship that Heaney writes about between himself and his father Paper The relationship that Heaney writes about between himself and his father Paper Essay Topic: Poetry Seamus Heaney Poems I am going to compare two different poems written by Seamus Heaney. The names of these two poems are Digging and Follower. Both of these poems were written when Seamus Heaney had started his career in poetry. Heaney was the eldest of nine children and grew up in poor conditions, as his father was a potato farmer, just as his forefathers. The poems are basically Heaneys autobiography, where he is explaining what happened in his past. Heaney was born when there were Catholic and Protestant riots were occurring and it was a troubled time for him and his family. The two poems are similar because they both describe Heaney at a young age, when he used to be tripping, falling, yapping always. This was meant to prove that Heaney was always behind his father, but the second poem has a real twist to it at the end, which I will describe to you further in to this essay. Heaney is probably writing this poem in his room, and looking out into his old farm which is bringing back his memories of being a child. His room would be dimly lit to show the bluntness in his vocabulary. This also depicts that fact that his language is not flowery, or there is no glorification of any part of his fathers job, but just going straight to the point. He does not in any way denigrate the job either, but just keeps it simply and straight to the point. I think that Heaney wouldve been in his dimly lit room (as explained above) and is picturing his father in a hat, with a grey coat on and his coarse boot nestled on the lug, against the inside knee was levered firmly. Heaneys language here conveys to us the point that he used language that reflects the traditional down-to-earth nature of his ancestors. What I mean here, is that most other writers would glorify these sentences and add extra vocabulary to add to the effect, but Heaneys draws in the readers interest by keeping it simple and concise. The relationship between Heaney and his father is exposed in the second line, The squat pen rests; snug as a gun, and it can be compared to line 4, Then the spade sinks Here, Heaney is trying to force through the point that his fathers profession was a farmer, and his weapon was a spade, whereas, Heaneys profession is a writer and his dangerous weapon is the pen. The pen also had enormous power and when the pen is used incorrectly, it can too cause damage. Heaneys pen gives him the eccentricity and power which he felt he lacked as a child due to the restricted conditions. The pen freed him from his restrictions that he had a child and the pen if offering him dangerous new possibilities. This emphasises the point that Heaney lacked attention and had wished to get it with the power of his pen. Heaney believes that the pen can be as powerful as the spade. This is proven in line 2 The squat pen rests; snug as a gun. This means that when the pen is not in use, it is just a potential threat, but when it is used incorrectly, it can be as dangerous as a gun, and a gun is surely more powerful than a spade. The relationship between him and his father is flowing at times, for example, when enjambment is used between lines five and six. My father digging. I look down Till his straining rump among the flowerbeds. The second stanza ends at the word down and the third stanza begins at the word Till. Enjambment is used to keep the rhythm of the poem continuously flowing and to keep the readers in the frame of the poem. Enjambment is also used to show that the poem is digging further into his memories. Heaney liked harsh and blunt sounds such as lug, coarse, nestled and heaving sods. These words dont have a squeaky sound to them, whereas, the words like nicking and slicing do. What I mean by blunt is that the words arent sharp or high, but easy to say, and uses less effort, meaning that more effort can be used in the work being done. The poem is basically about Heaneys admiration for his father. By god, the old man could handle a spade, Just like his old man My grandfather cut more turf in a day, than any other man in Toners Bog. In these quotes, he is portraying to us how much he admires his forefathers. He is exaggerating the fact that his grandfather cut more turf in a day than any other man in Toners Bog. He is exaggerating it because is substantiates that fact that his grandfather was the greatest potato farmer of all time, and that his speed and skill together was indestructible. He states that his grandfather is not any old potato farmer, but a very unique one indeed. The speed, I have verified above, but the skill of his grandfather-Nicking and slicing neatly. This is also Heaneys use of onomatopoeia nicking, sounds like its meaning; as does slicing. They are both quite gruesome words, but this depicts to us that the job of Heaneys forefather was gruesome and it also portrays the conditions that he wouldve lived in, being the eldest of nine children and being the son of a potato farmer. This exposes to us about Heaneys straight to the point thoughts, no matter how grisly his history may be, he will state it. Once I carried him milk in a bottle Corked sloppily with water. He straightened up to drink it, then fell to it straight away. This illustrates how devoted his forefathers were in their work. No other work could show that dedication, it was unparalleled. This is an example of Heaneys pride for his forefathers, not everyone would write in a poem how inspired they are by their forefathers. I think that Heaney is a bit ashamed of not being able to follow in their footsteps, But Ive no spade to follow like them. What Heaney means here is not that he has no spade, but he has no spade within him to carry on his fathers work, that he was not enough bottle to follow in their footsteps. Between my finger and my thumb, The squat pen rests. Ill dig with it Heaney is trying to convey the message that as his fathers profession was a farmer, he used the spade to dig for potatoes, but Heaney will use a pen to dig with it, meaning that he will continue his profession as a writer. Heaney believes the pen will give him that extra power but never that hardness and toughness that his forefathers had from their profession. I think that Heaney loves and respects his forefathers due to the amount of respect that he has given them in this poem. By God the old man could handle a spade, Just like his old man. This tells us that he admires his forefathers unbelievably, and that he is proud of them. I think that Heaney is not a bit monotonous, because each time he marvels at his forefathers, he is giving us something original, something new and interesting. He does say that he wanted to grow up and follow in his fathers footsteps, I wanted to grow up and plough All I ever did was follow. This shows us that he did want to be a farmer just like his forefathers, but he felt he lacked the physical strength, but he had the mental strength of being a writer. This explains that Heaney always wanted to be a farmer, but he felt he lacked the individuality that he needed and the confidence when he was a child, and he now feels a bit guilty not carrying on the family tradition. I think that Heaney felt inadequate and lost as a child and felt he lacked the attention that a child needed. That is why he felt he lacked the power of being a potato farmer, and that he would rather have had a stronger childhood to be a farmer, not a feeble and astray one as he has experienced. Heaney saw himself as a nuisance in both poems, but more so in the second poem. I stumbled in his hob nailed wake, Fell sometimes on the polished sod. This is a quote from the second poem elucidating the fact that he used to stumble on his fathers hard work. Heaneys language is blunt and matter of fact. Corked sloppily with water. He is just stating the obvious here, meaning that he is down to earth and likes to state what is there, and not exaggerate to give effect, but the structure and the way he has delivered this poem to us speaks for itself. Heaney also uses language that reflects the down-to-earth nature of his ancestors. The cold small of potato mould, the squelch and slap. Here is another example of onomatopoeia. Onomatopoeia is used to emphasise the meaning of the words to the reader, these words are one syllable words. One syllable words are easy to say and they get the meaning of the words of the reader straight away. One syllable words can also be used so that it takes less time to read, and it reflects the level of knowledge and education that his forefathers have in speaking. Another reason why one syllable words are used is because it shows us how little time these farmers have, and that they believe in a little less conversation, a little more action. His shoulders globed like a full sail strung. This is a simile which is used to compare his fathers shoulders with a sail. What he means here is that his shoulders were so muscular that they were comparable with a full sail strung. This also shows his admiration for his forefathers. How wonderful he thought they were; a pity that he was not as capable of doing physical activities as they were. Nar rowed and angled at the ground, Mapping the furrow exactly, this exemplifies to us the Heaneys father worked exactly and that he would calculate all of the angles and get the lifting of the turf exactly right. Heaney felt he was a nuisance following his father around all day, but then also felt proud to have a father whom he could follow around like that, All I ever did was follow, in his broad shadow round the farm. This is when Heaney would be looking up to his father. Heaney is looking up in not only the literal way, but also in character. He may also look up to his father in an idol like way. Comparing this to the last line of follower, it is like the falling of a god, as if the admiration empire for his father is crumbling. But today it is my father who keeps stumbling behind me, and will not go away. I dont think that Heaney is being spiteful, but there is a role reversal here. As, we have seen, in the first poem, Digging, he had great admiration for his forefathers. Towards the end of the second poem, the roles are reversed to show the change in Heaneys mind, Heaney now thinks that he is more powerful than his father due to the age difference. The last line can also be a metaphor. The meaning of this metaphor is that his father may be dead and the metaphorical part of this is that he may be dead, and his thoughts may keep lingering behind him, not his physical body itself. On the other hand, his father may be old and requires care. His father may loiter behind him and question everything he does asking whether he is doing it right or not, getting on his nerves. If he does get on his nerves, then I believe that he was being a bit spiteful, but I think that this is a metaphor and his father is dead, and his memories are lurking behind him. Now I am going to comment on other linguistic features, and the structure of this poem. Rhyme is used to bring out the points further. It helps the reader to enjoy the poem as well as understand the poem. Heaney also used rhythm in this poem. He uses a different rhythm for both Heaney and his father. I was a nuisance, tripping, falling, yapping always. That is the kind of rhythm used for Heaney. This is the rhythm which is used for Heaney because it is a bit rocky, just as his feelings, whereas the rhythm used for Heaneys father is Of reins, the sweating team turned around. The rhythm is much smoother for Heaneys father because his work is smooth and neat, whereas Heaney become s a bit spiteful at the end. Alliteration is also used in both poems. Alliteration is used because it makes the reader work just a bit harder, and it also draws in the readers attention better than other devices. Spade sinks, the alliteration is used here to show the smoothness when the spade sinks into to ground by his father, to depict how good of a farmer he is. Overall, I find Digging more effective than Follower. This is because the first poem is more emotional and he is comparing himself to his father more, and this reflects how he felt as a child. The second poem, Follower, is more technical, and readers prefer poems that are more emotional and describing, not technical and too straight to the point. I think that Heaney is very fond of his past and would like to re-live it; we can extrapolate this from the poems we have read. Both poems reveal that Heaney can remember his past very vividly and that he is a very good writer. He also considered himself as a lesser being most of the tie, I was a nuisance etc. He considered himself to not be as complex of a character of a being but a very simple person indeed. He was very humble in the way he wrote, not bragging on about himself, but showing the great admiration for his forefathers. I think that Heaney did not have a very simple relationship with his father. That was because there was not a lot of conversation between the two characters. Heaney was mainly seen and not heard in the poem, and his thoughts were mainly kept to himself as his father was too busy. The only part which I took into consideration was the change of roles at the end of Follower. That really showed that Heaney had a bit of a relationship with his father. Dead or not, he still remembers him and his memories will remain with Heaney forever.

World War II German Panther Medium Tank

World War II German Panther Medium Tank Armored vehicles known as tanks became crucial to the  efforts of France, Russia, and Britain to defeat the Triple Alliance of Germany, Austria-Hungary, and Italy in World War I. Tanks made it possible to shift the advantage from defensive maneuvers to offensive, and their use completely caught the Alliance off guard. Germany eventually developed a tank of their own, the A7V, but after the Armistice, all tanks in German hands  were confiscated  and  scrapped, and Germany was forbidden by various treaties to possess or build armored vehicles. All that changed with the rise to power by Adolph Hitler and the start of World War II. Design Development Development of the Panther began in 1941, following Germanys encounters with Soviet T-34 tanks in the opening days of Operation Barbarossa. Proving superior to their current tanks, the Panzer IV and Panzer III, the T-34 inflicted heavy casualties on German armored formations. That fall, following the capture of a T-34, a team was sent east to study the Soviet tank as a precursor to designing one superior to it. Returning with the results, Daimler-Benz (DB) and Maschinenfabrik Augsburg-Nà ¼rnberg AG (MAN) were ordered to design new tanks based on the study. In assessing the T-34, the German team found that the keys to its effectiveness were its 76.2 mm gun, wide road wheels, and sloping armor. Utilizing this data, DB and MAN delivered proposals to the Wehrmacht in April 1942. While the DB design was largely an improved copy of the T-34, MANs incorporated the T-34s strengths into a more traditional German design. Using a three-man turret (the T-34s fit two), the MAN design was higher and wider than the T-34 and was powered by a 690 hp gasoline engine. Though Hitler initially preferred the DB design, MANs was chosen because it used an existing turret design that would be quicker to produce. Once built, the Panther would be 22.5 feet long, 11.2 feet wide, and 9.8 feet high. Weighing around 50 tons, it was propelled by a V-12 Maybach gasoline-powered engine of about 690 hp. It reached a top speed of 34 mph, with a range of 155 miles, and held a crew of five men, which included the driver, radio-operator, commander, gunner, and loader. Its primary gun was a Rheinmetall-Borsig 1 x 7.5 cm KwK 42 L/70, with 2 x 7.92 mm Maschinengewehr 34 machine guns as the secondary armaments. It was built as a medium tank, a classification that stood somewhere between light, mobility-oriented tanks and heavily armored protection tanks. Production Following prototype trials at Kummersdorf in the fall of 1942, the new tank, dubbed Panzerkampfwagen V Panther, was moved into production. Due to the need for the new tank on the Eastern Front, production was rushed with the first units being completed that December. As a result of this haste, early Panthers were plagued by mechanical and reliability issues. At the Battle of Kursk in July 1943, more Panthers were lost to engine problems than to enemy action. Common issues included overheated engines, connecting rod and bearing failures, and fuel leaks. Additionally, the type suffered from frequent transmission and final drive breakdowns that proved difficult to repair. As a result, all Panthers underwent rebuilds at Falkensee in April and May 1943.  Subsequent upgrades to the design helped reduce or eliminate many of these issues.   While initial production of the Panther was assigned to MAN, demand for the type soon overwhelmed the companys resources.  As a result, DB, Maschinenfabrik Niedersachsen-Hannover, and Henschel Sohn all received contracts to build the Panther.  During the course of the war, around 6,000 Panthers would be constructed, making the tank the third most-produced vehicle for the Wehrmacht behind the Sturmgeschà ¼tz III and Panzer IV. At its peak in September 1944, 2,304 Panthers were operational on all fronts. Though the German government set ambitious production goals for Panther construction, these were seldom met due to Allied bombing raids repeatedly targeting key aspects of the supply chain, such as the Maybach engine plant and a  number of Panther factories themselves. Introduction The Panther entered service in January 1943 with the formation of Panzer Abteilung (Battalion) 51. After equipping Panzer Abteilung 52 the following month, increased numbers of the type were sent to frontline units early that spring. Viewed as a key element of Operation Citadel on the Eastern Front, the Germans delayed opening the Battle of Kursk until sufficient numbers of the tank were available. First seeing major combat during the fighting, the Panther initially proved ineffective due to numerous mechanical issues. With the correction of the production-related mechanical difficulties, the Panther became highly popular with German tankers and a fearsome weapon on the battlefield. While the Panther was initially intended to only equip one tank battalion per panzer division, by June 1944, it accounted for nearly half of German tank strength on both the eastern and western fronts. The Panther was first used against US and British forces at Anzio in early 1944. As it only appeared in small numbers, US and British commanders believed it to be a heavy tank that would not be built in large numbers. When Allied troops landed in Normandy that June, they were shocked to find that half the German tanks in the area were Panthers. Greatly outclassing the M4 Sherman, the Panther with its high-velocity 75mm gun inflicted heavy casualties on Allied armored units and could engage at a longer range than its foes. Allied tankers soon found that their 75mm guns were incapable of penetrating the Panthers frontal armor and that flanking tactics were required. Allied Response To combat the Panther, US forces began deploying Shermans with 76mm guns, as well as the M26 Pershing heavy tank and tank destroyers carrying 90mm guns. British units frequently fitted Shermans with 17-pdr guns (Sherman Fireflies) and deployed increasing numbers of towed anti-tank guns. Another solution was found with the introduction of the Comet cruiser tank, featuring a 77mm high-velocity gun, in December 1944. The Soviet response to the Panther was faster and more uniform, with the introduction of the T-34-85. Featuring an 85mm gun, the improved T-34 was nearly the equal of the Panther. Though the Panther remained slightly superior, high Soviet production levels quickly allowed large numbers of T-34-85s to dominate the battlefield. In addition, the Soviets developed the heavy IS-2 tank (122mm gun) and the SU-85 and SU-100 anti-tank vehicles to deal with the newer German tanks. Despite the Allies efforts, the Panther remained arguably the best medium tank in use by either side. This was largely due to its thick armor and ability to pierce the armor of enemy tanks at ranges up to 2,200 yards. Postwar The Panther remained in German service until the end of the war. In 1943, efforts were made to develop the Panther II. While similar to the original, the Panther II was intended to utilize the same parts as the Tiger II heavy tank to ease maintenance for both vehicles. Following the war, captured Panthers were briefly used by the French 503e Rà ©giment de Chars de Combat. One of the iconic tanks of World War II, the Panther influenced a number of postwar tank designs, such as the French AMX 50.

Lessons Learned from the Enron Scandal Term Paper

Lessons Learned from the Enron Scandal - Term Paper Example The bankruptcy of such a big organization is regarded as the greatest setback in American history. The dissolution of Enron was the result of its own false practices illegal dealings of projects and not showing their debts on their company’s accounts. (Project 2000_25_Corporate) It was regarded as the greatest failure in terms of audit. Enron was established in 1985 by Kenneth Lay after the merger of Houston Natural Gas and Inter North. This merger created the largest gas pipeline system in America. In the 1990’s Kenneth Lay took an initiative to sell the electricity at market prices and the resulting markets helped him to sell the electricity at higher rates as a result increasing their income. Enron not only delivered natural gas but also became a market middleman for energy and brought the buyers and sellers of energy on one platform. Enron in just 15 years reached such a position where it became America’s seventh biggest company which employed 21,000 employee s in more than forty countries. (Enron scandal-at-a-glance, 2002) Enron became dominant in the trading of energy contracts and financial instruments known as Derivatives. By 1992, Enron became the largest seller of natural gas in North America with earnings of $122 million. In the late 1990’s Enron was considered as the best in the world as it controlled twenty five percent of all electricity and natural gas contracts. In November 1999, Enron’s online website was established which helped the company to manage its contracts more efficiently. This website of the corporation in no time became the largest e-business site of the world. Enron also invested in physical facilities. Enron in the beginning was an insurance company. For further development of the company, Enron purchased a number of assets which included gas pipelines, electricity plants, water plants and broadband services all over the world. The company also incurred revenue by dealing in the same products and services in which it had been involved. The stock of Enron rose from the beginning of the 1990’s until 1998 by 311% which was a remarkable increase in the rate of growth. Apart from that Enron was rated as the most innovative corporation in America, in the survey of Fortune’s most Admired Companies. After many years Jeffery Skilling was hired who developed the idea of using such an accounting system which could hide debts in billions from the failed deals. Not only him but Andrew Fastow Chief Financial Officer and many other executives misguided the board of directors of the Enron company. The shareholders of the Enron Company lost 11$ billion which was as high as US$90 per share in the middle of 2000 but fell to less than 1$ at the end of Nov 2001.As a result of which the U.S. Securities and Exchange Commission started to investigate the matter. The decline of Enron started when its investors became known of the â€Å"off balance sheet† partnerships that were h iding billions of dollars of debts. One of the deals with Blockbuster Inc. which was a video rental company to provide movies on the internet was also cancelled in March. Moreover the rival company Dynegy offered to purchase the company and the deal was finalized on December 2, 2001. The Enron Company finally filed for the bankruptcy of the company. In the U.S. history Enron was the largest corporate bankruptcy until WorldCom’s was declared bankrupt the next year. Moreover there were many executives who were blamed for a number of charges and were then sentenced to prison. Moreover, Arthur Andersen the auditor of the corporation

Cross Cultural Managment Essay Example | Topics and Well Written Essays - 1500 words

Cross Cultural Managment - Essay Example In this context, therefore, cultural intelligence can be described as the ability of individuals in the working place to develop a sensible working condition despite their affiliations (Ang & Livermore, pp.38; Earley, Ang & Tan, pp.3). This essay shall aim at analyzing two articles in an attempt to find out which article is the most applicable to proving the importance of ‘Cultural Intelligence’ (CQ) to the manager of Global Alliances. The essay shall incorporate both theoretical and practical justifications on the importance of ‘Cultural Intelligence’ (CQ) in any organization. According to Triandis, just like in Peterson, (pp.177) and Lundby (pp.301), cultural intelligence is vital for survival of any organization. In his work, he indicates that no flourishing interaction can exist without the staff embracing the aspects of cultural intelligence. Triandis (pp.20) indicates that if the organization has to be successful in inculcating feelings of cultural int elligence among the workers, they have to be keen to detect any kind of flaws that might be existent in the workplace that might harbor successful incorporation of basics that can inculcate roots of cultural intelligence among the workers. ... This entails the ability of the individuals to understand the perceptions and behaviors of the concerned parties in regard to their cultural backgrounds. Of essence, he emphasizes that in the case of varying cultures, individuals must be quick to focus more on the context of their workforce unlike content of what they might have communicated. At times individuals are likely to behave according to the way other people behave in varying cultures, a factor Triandis (pp.20) refers to as ideocentrism. He also explains the concept allocentrism that may alter thriving of cultural intelligence in the workplace. On a practical aspect, in the case of a manager, it would be beneficial if one assesses all kinds of information given by the concerned parties, before making a judgment especially if disputes exist between sections of employees. Collecting tangible evidence unlike insinuations or clues would be beneficial to the manager. Secondly, culturally intelligent persons must be keen to identi fy behaviors that exist in the tough situations in the workplace (Livermore, pp.53). This interprets that, in the course of coexisting in the working environment, there are higher chances that individuals may conflict as a result of interactions in the society. Triandis (pp.22) indicates that chances are probable that individuals are likely to conflict in the quest to make their opinions heard in the workplace. Practically, the managers may consider gathering all kinds of information that would allow them make judgments that are biased, but for the good of the entire workplace. On another view point, a culturally intelligent person is one that is able to handle circumstances that emanate from cultural variances. Triandis

Visual Arts and Film Studies Essay Example | Topics and Well Written Essays - 2250 words

Visual Arts and Film Studies - Essay Example Discussion of Greek architecture and the various stages of development that it went through and the impact of those developments on their art and artifacts is the focal point of this paper. To attain the objective and to compare the variation in art pertaining to two different periods of the same civilization, pottery has been decided to be focused upon. Tabular Comparison Part II Visual Analysis The above figure is a front view comparison of the two pieces of pottery selected for this paper. In the above figure the two pieces of art are distinguished and deconstructed into 4 major and prominent factions from the front view. Tabular comparison covers the differences between the two pieces of art in detail; however a frontal view comparison is as follows. The two pieces of art can be distinguished into A= Neck, B= Handle, C= Belly and D= Base. In figure A it can be observed that the neck of the vase is slimmer and compliments the imagery that is present drawn on the body of the vase w hereas in figure B the neck is wider and once again provides a balance symmetry with the overall orientation of the amphora (Scott, 2004). The handles in both the pieces of art are different in their structure, shape and inclination and perhaps purpose as well. In figure A we can see that the handles are an extension of the vase and are not an additional inclusion in the structure of the pot. The handles are part of the design of the vase. In comparison to Fig A, handles in figure B are not highlighted in the frontal view. From the front view only edges of the handles are observable while in figure A frontal view clearly shows the features of the handles (Scott, 2004). Part C in both the pots is the Belly. In Figure A, belly is circular in its shape and is once again utilized by the artist to compliment the image that has been drawn on the body. On the other hand in Fig B the belly is elongated and is oval in its shape. Belly comprise the main proportion of the entire structure in b oth the pots but Figure A has a more radial shape of the belly in contrast to Fig B that is slender in its orientation. Part D in both the pots, as highlighted above is the base of the figure. There are similarities in the base of both the pieces of art as can be observed. The base appears to be solid and flat in both the pieces of art. Another aspect to be observed from a technical view point is the width of the base in both the figures is in accordance with the shape and size of the entire art work. In figure A the base is wider than that in Figure B and this variation in width can be associated to the fact that bellies in both the figures occupy a different volume and thus they require different widths of bases to form a balanced art structure (Scott, 2004). In the above table the two art works are deconstructed into various observable components. The differences in the orientation shape and design of the two art works clearly depicts the transformation that the art work and civi lization has come across over the passage of time (Lynch, 2005). Figura Activa refers to the active image that can be observed prominently in a piece of art. For figure A figura activa is identified to be an octopus. While in Figure B no prominent character can be identified however circular lines along the horizontal axis are the only notable existence in the art work. Mesomorph is referred to as the overall expansion of the shape of an art