Preface	7
	Contents	9
	Introduction	13
	Interest Rates and Related Contracts	16
	Zero-Coupon Bonds	16
	Interest Rates	17
	Market Example: LIBOR	18
	Simple vs. Continuous Compounding	19
	Forward vs. Future Rates	20
	Money-Market Account and Short Rates	20
	Proxies for the Short Rate	21
	Coupon Bonds, Swaps and Yields	22
	Fixed Coupon Bonds	22
	Floating Rate Notes	23
	Interest Rate Swaps	23
	Yield and Duration	26
	Yield-to-Maturity	26
	Duration and Convexity	27
	Market Conventions	28
	Day-Count Conventions	28
	Coupon Bonds	29
	Accrued Interest, Clean Price and Dirty Price	29
	Yield-to-Maturity	30
	Caps and Floors	30
	Caps	31
	Floors	31
	Caps, Floors and Swaps	32
	Black's Formula	32
	Swaptions	33
	Black's Formula	35
	Exercises	35
	Notes	38
	Estimating the Term-Structure	40
	A Bootstrapping Example	40
	Non-parametric Estimation Methods	45
	Bond Markets	46
	Money Markets	47
	Problems	49
	Parametric Estimation Methods	49
	Estimating the Discount Function with Cubic B-splines	49
	Smoothing Splines	54
	Exponential-Polynomial Families	60
	Principal Component Analysis	62
	Principal Components of a Random Vector	62
	Sample Principle Components	63
	PCA of the Forward Curve	64
	Correlation	66
	Exercises	67
	Notes	68
	Arbitrage Theory	69
	Stochastic Calculus	69
	Stochastic Integration	70
	Quadratic Variation and Covariation	71
	Itô's Formula	72
	Stochastic Differential Equations	73
	Stochastic Exponential	74
	Financial Market	75
	Self-Financing Portfolios	75
	Numeraires	76
	Arbitrage and Martingale Measures	77
	Martingale Measures	78
	Market Price of Risk	79
	Admissible Strategies	80
	The First Fundamental Theorem of Asset Pricing	80
	Hedging and Pricing	81
	Complete Markets	81
	Arbitrage Pricing	84
	Exercises	85
	Notes	87
	Short-Rate Models	88
	Generalities	88
	Diffusion Short-Rate Models	89
	Examples	91
	Inverting the Forward Curve	92
	Affine Term-Structures	93
	Some Standard Models	94
	Vasicek Model	94
	CIR Model	96
	Dothan Model	97
	Ho-Lee Model	98
	Hull-White Model	99
	Exercises	100
	Notes	101
	Heath-Jarrow-Morton (HJM) Methodology	102
	Forward Curve Movements	102
	Absence of Arbitrage	104
	Short-Rate Dynamics	105
	HJM Models	106
	Proportional Volatility	107
	Fubini's Theorem	108
	Exercises	111
	Notes	112
	Forward Measures	113
	T-Bond as Numeraire	113
	Bond Option Pricing	117
	Example: Vasicek Short-Rate Model	118
	Black-Scholes Model with Gaussian Interest Rates	118
	Example: Black-Scholes-Vasicek Model	121
	Exercises	122
	Notes	124
	Forwards and Futures	125
	Forward Contracts	125
	Futures Contracts	126
	Interest Rate Futures	127
	Forward vs. Futures in a Gaussian Setup	128
	Exercises	129
	Notes	130
	Consistent Term-Structure Parametrizations	131
	Multi-factor Models	131
	Consistency Condition	133
	Affine Term-Structures	135
	Polynomial Term-Structures	136
	Special Case: m=1	137
	General Case: m>=1	139
	Exponential-Polynomial Families	142
	Nelson-Siegel Family	142
	Svensson Family	143
	Exercises	146
	Notes	148
	Affine Processes	150
	Definition and Characterization of Affine Processes	150
	Canonical State Space	153
	Discounting and Pricing in Affine Models	158
	Examples of Fourier Decompositions	164
	Bond Option Pricing in Affine Models	168
	Example: Vasicek Short-Rate Model	169
	Example: CIR Short-Rate Model	170
	Heston Stochastic Volatility Model	173
	Affine Transformations and Canonical Representation	175
	Existence and Uniqueness of Affine Processes	178
	On the Regularity of Characteristic Functions	180
	Auxiliary Results for Differential Equations	184
	Some Invariance Results	184
	Some Results on Riccati Equations	187
	Proof of Theorem 10.3	192
	Exercises	193
	Notes	201
	Market Models	203
	Heuristic Derivation	203
	LIBOR Market Model	205
	LIBOR Dynamics Under Different Measures	207
	Implied Bond Market	207
	Implied Money-Market Account	210
	Swaption Pricing	212
	Forward Swap Measure	213
	Analytic Approximations	215
	Monte Carlo Simulation of the LIBOR Market Model	216
	Volatility Structure and Calibration	218
	Principal Component Analysis	218
	Calibration to Market Quotes	219
	Continuous-Tenor Case	225
	Exercises	227
	Notes	229
	Default Risk	230
	Default and Transition Probabilities	230
	Structural Approach	232
	Intensity-Based Approach	234
	Construction of Doubly Stochastic Intensity-Based Models	240
	Computation of Default Probabilities	241
	Pricing Default Risk	241
	Zero Recovery	242
	Partial Recovery at Maturity	243
	Partial Recovery at Default	243
	Measure Change	245
	Exercises	247
	Notes	248
	References	249
	Index	256