《金融期货与期权》（英文版）Chapter 25 Swaps revisited

25.1 Chapter 25 Swaps revisited Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 25.1 Chapter 25 Swaps Revisited

25.2 Valuation of swaps The standard approach is to assume that forward rates will 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, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 25.2 Valuation of Swaps • The standard approach is to assume that forward rates will be realized • This works for plain vanilla interest rate and plain vanilla currency swaps, but does not necessarily work for non￾standard swaps

25.3 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 exchanging the 3-month LIBOR for 3-month T-Bill rate be valued Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 25.3 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 exchanging the 3-month LIBOR for 3-month T-Bill rate be valued?

25.4 Compounding swaps 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. 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, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 25.4 Compounding Swaps • 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. 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

25.5 Currency swaps Standard currency swaps can be valued using the"assume forward LIBOR rate are realized”ru|e. Sometimes 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, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 25.5 Currency Swaps • Standard currency 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 B

25.6 More complex swaps LIBOR-in-arrears swaps CMS and CMt swaps Differential swaps To value these we assume that the realized rate is the forward rate plus a convexity adjustment Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 25.6 More Complex Swaps – LIBOR-in-arrears swaps – CMS and CMT swaps – Differential swaps To value these we assume that the realized rate is the forward rate plus a convexity adjustment

25.7 Equity swaps Total return on an equity index 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, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 25.7 Equity Swaps • Total return on an equity index 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

25.8 Swaps with Embedded Options Accrual swaps Cancelable swaps Cancelable compounding swaps Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 25.8 Swaps with Embedded Options • Accrual swaps • Cancelable swaps • Cancelable compounding swaps

25.9 Other Swaps Indexed principal swap Commodity swap Volatility swap Bizzarre deals for example the p&G 5/30 swap Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 25.9 Other Swaps • Indexed principal swap • Commodity swap • Volatility swap • Bizzarre deals: for example the P&G 5/30 swap