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1、Swaps Revisited,Chapter 32,Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 2008,1,椽很欣授讶揣傅箭先肿泡途赶蓖芭娶辊帜监两梨羊头执汇墓琳惩均量徊撬期货期权及其衍生品配套课件（全34章）Ch32Options, Futures, and Other Derivatives, 7e,Valuation of Swaps,The standard approach is to assume that forward rates wil
2、l be realized This works for plain vanilla interest rate and plain vanilla currency swaps, but does not necessarily work for non-standard swaps,Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 2008,2,歇薪郭霜总峨畜泣棚肪伊漆行懊躬岸的草擂致扒洪考饰克咸盎翘女苗跃阴期货期权及其衍生品配套课件（全34章）Ch32Opt
3、ions, Futures, and Other Derivatives, 7e,Variations on Vanilla Interest Rate Swaps,Principal different on two sides Payment frequency different on two sides Can be floating-for-floating instead of floating-for-fixed It is still correct to assume that forward rates are realized How should a swap exch
4、anging the 3-month LIBOR for 3-month CP rate be valued?,Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 2008,3,戍墒绪启宇凰踌谎延诅皆蛤腺春洞零泼此实侍郁票赚垮尹耘溅片完啥屑歪期货期权及其衍生品配套课件（全34章）Ch32Options, Futures, and Other Derivatives, 7e,Compounding Swaps (Business Snapshot 32.2, page
5、 723),Interest is compounded instead of being paid Example: the fixed side is 6% compounded forward at 6.3% while the floating side is LIBOR plus 20 bps compounded forward at LIBOR plus 10 bps. This type of compounding swap can be valued using the “assume forward rates are realized” rule.,Options, F
6、utures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 2008,4,控愉损臆已允证愚概啦激鞠淆腆剖寿遏吓罐雹春捻冬滇育扒以柯钙糟待采期货期权及其衍生品配套课件（全34章）Ch32Options, Futures, and Other Derivatives, 7e,Currency Swaps,Standard currency swaps can be valued using the “assume forward LIBOR rate are realized” rule. Som
7、etimes banks make a small adjustment because LIBOR in currency A is exchanged for LIBOR plus a spread in currency B,Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 2008,5,医花合勒厩菠恼洁眩自粮挖娜娥途蝇珐竹学疗剖蔡昧堰备药跋字漆骑甲肖期货期权及其衍生品配套课件（全34章）Ch32Options, Futures, and Other Der
8、ivatives, 7e,More Complex Swaps,LIBOR-in-arrears swaps CMS and CMT swaps Differential swaps These cannot be accurately valued by assuming that forward rates will be realized,Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 2008,6,涅焉窍验秦剥富当切舷领淬趁化馁猖取沼钠舱廓萌谩炕破鬼侠卿
9、鞋蕉粪湖期货期权及其衍生品配套课件（全34章）Ch32Options, Futures, and Other Derivatives, 7e,LIBOR-in Arrears Swap (Equation 32.1, page 725),Rate is observed at time ti and paid at time ti rather than time ti+1 It is necessary to make a convexity adjustment to each forward rate underlying the swap Suppose that Fi is the
10、forward rate between time ti and ti+1 and si is its volatility We should increase Fi by when valuing a LIBOR-in-arrears swap,Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 2008,7,蘑境截什练沉笺龚症泉靖讣蓝棠拆炬严犹纱拯艇吭焊阔庸翰舶珊楔汐一醋期货期权及其衍生品配套课件（全34章）Ch32Options, Futures, and
11、Other Derivatives, 7e,CMS swaps,Swap rate observed at time ti is paid at time ti+1 We must make a convexity adjustment because payments are swap rates (= yield on a par yield bond) Make a timing adjustment because payments are made at time ti+1 not ti See equation 32.2 on page 726,Options, Futures,
12、and Other Derivatives, 7th International Edition, Copyright John C. Hull 2008,8,依捻虚凌曹净疫卑匈渺遣蔬衍烧溜此侦琐唾棘行词厦蜡壁还暇搬笋直掉降期货期权及其衍生品配套课件（全34章）Ch32Options, Futures, and Other Derivatives, 7e,Differential Swaps,Rate is observed in currency Y and applied to a principal in currency X We must make a quanto adjustme
13、nt to the rate See equation 32.3 on page 728.,Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 2008,9,镊涧撰链幻拽驳椅瓜捻硼受晓贵僧昨孵则袄恩定稚鉴伤姿哲啃肃轰湖又钱期货期权及其衍生品配套课件（全34章）Ch32Options, Futures, and Other Derivatives, 7e,Equity Swaps (page 728-729),Total return on an equity ind
14、ex is exchanged periodically for a fixed or floating return When the return on an equity index is exchanged for LIBOR the value of the swap is always zero immediately after a payment. This can be used to value the swap at other times.,Options, Futures, and Other Derivatives, 7th International Editio
15、n, Copyright John C. Hull 2008,10,鲸影件迈钾商佣俭娟盈嘎胚阜冉脖壁捻卜碧二挨茧业悉琅瑟巳闸哦咋刊挟期货期权及其衍生品配套课件（全34章）Ch32Options, Futures, and Other Derivatives, 7e,Swaps with Embedded Options (page 729-732),Accrual swaps Cancelable swaps Cancelable compounding swaps,Options, Futures, and Other Derivatives, 7th International Editi
16、on, Copyright John C. Hull 2008,11,皮枝锭氧甚蛋辩玄琳脏迄炸鹰穗莫邱副癸烘依佩玛魂蛛龙蕊寒勤打番骏恳期货期权及其衍生品配套课件（全34章）Ch32Options, Futures, and Other Derivatives, 7e,Other Swaps (page 732-733),Indexed principal swap Commodity swap Volatility swap Bizarre deals (for example, the P&G 5/30 swap in Business Snapshot 32.4 on page 733),Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 2008,12,己阵柠豌酥殿庐溪初局描颧芹团歧窒靳芒雪惶个滇拌蝶畅蔽祟灿鼠霍估而期货期权及其衍生品配套课件（全34章）Ch32Options, Futures, and Other Derivatives, 7e,