Contents 1 Introduction 2 2 Fixed-income Pricing in a Diffusion Setting 3 21 The Term Structure......·········· 4 2.2 FIS with Deterministic Payoffs.. 5 2.3 FIS with State-dependent Payoffs 5 2.4 FIS with Stopping Times..············ 7 3 DTSMs for Default-free Bonds 9 3.1One-factor DTSMs...·...·....·····.· 9 3.2 Multi--factor DTSMs·....············· 12 4 DTSMs with Jump Diffusions 16 5 DTSMs with Regime Shifts 17 6 DTSMs with Rating Migrations 20 6.1 Fractional Recovery of Market Value....·.,.·····. 21 6.2 Fractional Recovery of Par,Payable at Maturity........ 24 6.3 Fractional Recovery of Par,Payable at Default ........ 25 6.4 Pricing Defaultable Coupon Bonds.......... 25 6.5 Pricing Eurodollar Swaps..........···. 26 7 Pricing of Fixed-Income Derivatives 27 7.1 Derivatives Pricing using DTSMs 27 7.2 Derivatives Pricing using Forward Rate Models 29 7.3 Defaultable Forward Rate Models with Rating Migrations 31 7.4 The LIBOR Market Model..·················· 34 7.5 The Swaption Market Model...·.........···... 38 1Contents 1 Introduction 2 2 Fixed-income Pricing in a Diffusion Setting 3 2.1 The Term Structure . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 FIS with Deterministic Payoffs . . . . . . . . . . . . . . . . . . 5 2.3 FIS with State-dependent Payoffs . . . . . . . . . . . . . . . . 5 2.4 FIS with Stopping Times . . . . . . . . . . . . . . . . . . . . . 7 3 DTSMs for Default-free Bonds 9 3.1 One-factor DTSMs ........................ 9 3.2 Multi-factor DTSMs . . . . . . . . . . . . . . . . . . . . . . . 12 4 DTSMs with Jump Diffusions 16 5 DTSMs with Regime Shifts 17 6 DTSMs with Rating Migrations 20 6.1 Fractional Recovery of Market Value . . . . . . . . . . . . . . 21 6.2 Fractional Recovery of Par, Payable at Maturity . . . . . . . . 24 6.3 Fractional Recovery of Par, Payable at Default . . . . . . . . . 25 6.4 Pricing Defaultable Coupon Bonds . . . . . . . . . . . . . . . 25 6.5 Pricing Eurodollar Swaps . . . . . . . . . . . . . . . . . . . . . 26 7 Pricing of Fixed-Income Derivatives 27 7.1 Derivatives Pricing using DTSMs . . . . . . . . . . . . . . . . 27 7.2 Derivatives Pricing using Forward Rate Models . . . . . . . . 29 7.3 Defaultable Forward Rate Models with Rating Migrations . . 31 7.4 The LIBOR Market Model . . . . . . . . . . . . . . . . . . . . 34 7.5 The Swaption Market Model . . . . . . . . . . . . . . . . . . . 38 1