Preface |
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v | |
Introduction |
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vii | |
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xv | |
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xvii | |
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1 A Review of Stochastic Calculus |
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1 | (20) |
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1 | (2) |
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1.2 Stochastic Integration |
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3 | (5) |
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1.3 Definite Stochastic Integral |
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8 | (2) |
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10 | (3) |
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13 | (3) |
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16 | (5) |
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2 A Review of Black-Scholes Pricing and Hedging |
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21 | (18) |
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21 | (2) |
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2.2 Market Model and Self-Financing Portfolio |
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23 | (1) |
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24 | (1) |
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25 | (5) |
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30 | (7) |
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37 | (2) |
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3 Short-Term Interest Rate Models |
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39 | (16) |
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3.1 Mean-Reverting Models |
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39 | (5) |
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3.2 Constant Elasticity of Variance (CEV) Models |
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44 | (1) |
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3.3 Time-Dependent Affine Models |
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45 | (1) |
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3.4 Calibration of the Vasicek Model |
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45 | (2) |
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47 | (3) |
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50 | (5) |
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4 Pricing of Zero-Coupon and Coupon Bonds |
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55 | (20) |
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4.1 Definition and Basic Properties |
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55 | (4) |
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59 | (3) |
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4.3 Probabilistic Solution |
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62 | (5) |
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4.4 Numerical Simulations |
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67 | (2) |
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4.5 Bond Prices and Yield Data |
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69 | (1) |
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70 | (5) |
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5 Forward Rates and Swap Rates |
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75 | (22) |
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75 | (2) |
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5.2 Instantaneous Forward Rates |
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77 | (6) |
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83 | (3) |
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86 | (4) |
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90 | (2) |
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92 | (5) |
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6 Curve Fitting and a Two-Factor Model |
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97 | (22) |
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6.1 Parametrization of Forward Rates |
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97 | (5) |
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6.2 Fitting Curve Models to Market Data |
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102 | (2) |
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104 | (1) |
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6.4 The Correlation Problem |
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105 | (2) |
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107 | (8) |
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115 | (4) |
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119 | (18) |
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119 | (2) |
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121 | (4) |
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7.3 HJM-Vasicek Forward Rates |
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125 | (3) |
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7.4 Markov Property of Short Rates |
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128 | (4) |
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132 | (3) |
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135 | (2) |
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8 Forward Measures and Derivative Pricing |
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137 | (38) |
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8.1 Forward Rate Measures |
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137 | (7) |
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8.2 Dynamics under the Forward Measure |
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144 | (5) |
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149 | (3) |
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8.4 Vasicek Bond Option Pricing |
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152 | (3) |
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8.5 Forward Swap Measures |
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155 | (8) |
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163 | (12) |
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9 Pricing of Caps and Swaptions |
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175 | (38) |
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175 | (6) |
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181 | (4) |
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9.3 Black Swaption Pricing |
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185 | (3) |
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9.4 Swaption Pricing in the BGM Model |
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188 | (5) |
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9.5 Calibration of the BGM Model |
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193 | (3) |
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196 | (17) |
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213 | (18) |
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10.1 Survival Probabilities |
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213 | (2) |
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215 | (3) |
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218 | (2) |
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10.4 Estimating Default Rates |
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220 | (2) |
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10.5 Credit Default Swaps |
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222 | (3) |
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225 | (6) |
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11 Appendix: Mathematical Tools |
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231 | (8) |
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12 Solutions to the Exercises |
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239 | (104) |
Bibliography |
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343 | (4) |
Index |
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347 | (6) |
Author Index |
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353 | |