1、Options, Futures, and Other Derivatives, 6th Edition, Copyright John C. Hull 200530.1Chapter 30Swaps RevisitedOptions, Futures, and Other Derivatives, 6th Edition, Copyright John C. Hull 200530.2Valuation of SwapsThe standard approach is to assume that forward rates will be realizedThis works for pl

2、ain vanilla interest rate and plain vanilla currency swaps, but does not necessarily work for non-standard swapsOptions, Futures, and Other Derivatives, 6th Edition, Copyright John C. Hull 200530.3Variations on Vanilla Interest Rate SwapsPrincipal different on two sidesPayment frequency different on

3、 two sidesCan be floating-for-floating instead of floating-for-fixedIt is still correct to assume that forward rates are realizedHow should a swap exchanging the 3-month LIBOR for 3-month CP rate be valued?Options, Futures, and Other Derivatives, 6th Edition, Copyright John C. Hull 200530.4Compoundi

4、ng Swaps (Business Snapshot 30.2, page 699)Interest is compounded instead of being paidExample: 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 r

5、ates are realized” rule. This is because we can enter into a series of forward contracts that have the effect of exchanging cash flows for their values when forward rates are realized.Options, Futures, and Other Derivatives, 6th Edition, Copyright John C. Hull 200530.5Currency SwapsStandard currency

6、 swaps can be valued using the “assume forward LIBOR rate are realized” rule.Sometimes banks make a small adjustment because LIBOR in currency A is exchanged for LIBOR plus a spread in currency BOptions, Futures, and Other Derivatives, 6th Edition, Copyright John C. Hull 200530.6More Complex SwapsLI

7、BOR-in-arrears swapsCMS and CMT swapsDifferential swapsThese cannot be accurately valued by assuming that forward rates will be realizedOptions, Futures, and Other Derivatives, 6th Edition, Copyright John C. Hull 200530.7LIBOR-in Arrears Swap (Equation 30.1, page 701)Rate is observed at time ti and

8、paid at time ti rather than time ti+1It is necessary to make a convexity adjustment to each forward rate underlying the swapSuppose that Fi is the forward rate between time ti and ti+1 and si is its volatilityWe should increase Fi bywhen valuing a LIBOR-in-arrears swapOptions, Futures, and Other Der

9、ivatives, 6th Edition, Copyright John C. Hull 200530.8CMS swapsSwap rate observed at time ti is paid at time ti+1We 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 30.2 o

10、n page 702 Options, Futures, and Other Derivatives, 6th Edition, Copyright John C. Hull 200530.9Differential SwapsRate is observed in currency Y and applied to a principal in currency XWe must make a quanto adjustment to the rateSee equation 30.3 on page 704.Options, Futures, and Other Derivatives,

11、6th Edition, Copyright John C. Hull 200530.10Equity Swaps (705)Total return on an equity index is exchanged periodically for a fixed or floating returnWhen 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, 6th Edition, Copyright John C. Hull 200530.11Swaps with Embedded Options (708)Accrual swapsCancelable swapsCancelable compounding swapsOptions, Futures, and Other Derivatives, 6th Edition