## Dynamic Asset Pricing TheoryThis is a thoroughly updated edition of Readers will be particularly intrigued by this latest edition's most significant new feature: a chapter on corporate securities that offers alternative approaches to the valuation of corporate debt. Also, while much of the continuous-time portion of the theory is based on Brownian motion, this third edition introduces jumps--for example, those associated with Poisson arrivals--in order to accommodate surprise events such as bond defaults. Applications include term-structure models, derivative valuation, and hedging methods. Numerical methods covered include Monte Carlo simulation and finite-difference solutions for partial differential equations. Each chapter provides extensive problem exercises and notes to the literature. A system of appendixes reviews the necessary mathematical concepts. And references have been updated throughout. With this new edition, |

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### Contents

B Forward Prices | 169 |

C Futures and Continuous Resettlement | 171 |

D ArbitrageFree Futures Prices | 172 |

E Stochastic Volatility | 174 |

F Option Valuation by Transform Analysis | 178 |

G American Security Valuation | 182 |

H American Exercise Boundaries | 186 |

I Lookback Options | 189 |

22 | |

24 | |

26 | |

27 | |

G Arbitrage and Martingale Measures | 28 |

H Valuation of Redundant Securities | 30 |

I American Exercise Policies and Valuation | 31 |

J Is Early Exercise Optimal? | 35 |

Exercises | 37 |

Notes | 45 |

The Dynamic Programming Approach | 49 |

B FirstOrder Bellman Conditions | 50 |

C Markov Uncertainty | 51 |

D Markov Asset Pricing | 52 |

F Markov ArbitrageFree Valuation | 55 |

G Early Exercise and Optimal Stopping | 56 |

Exercises | 58 |

Notes | 63 |

The InfiniteHorizon Setting | 65 |

B Dynamic Programming and Equilibrium | 69 |

C Arbitrage and State Prices | 70 |

D Optimality and State Prices | 71 |

E MethodofMoments Estimation | 73 |

Exercises | 76 |

Notes | 78 |

CONTINUOUSTIME MODELS | 81 |

The BlackScholes Model | 83 |

B Martingale Trading Gains | 85 |

C Ito Prices and Gains | 86 |

D Itos Formula | 87 |

E The BlackScholes OptionPricing Formula | 88 |

First Try | 90 |

G The PDE for ArbitrageFree Prices | 92 |

H The FeynmanKac Solution | 93 |

I The Multidimensional Case | 94 |

Exercises | 97 |

Notes | 100 |

State Prices and Equivalent Martingale Measures | 101 |

B Numeraire Invariance | 102 |

C State Prices and Doubling Strategies | 103 |

D Expected Rates of Return | 106 |

E Equivalent Martingale Measures | 108 |

F State Prices and Martingale Measures | 110 |

G Girsanov and Market Prices of Risk | 111 |

H BlackScholes Again | 115 |

I Complete Markets | 116 |

J Redundant Security Pricing | 119 |

K Martingale Measures From No Arbitrage | 120 |

L Arbitrage Pricing with Dividends | 123 |

M Lumpy Dividends and Term Structures | 125 |

N Martingale Measures Infinite Horizon | 127 |

Exercises | 128 |

Notes | 131 |

TermStructure Models | 135 |

A The Term Structure | 136 |

B OneFactor TermStructure Models | 137 |

C The Gaussian SingleFactor Models | 139 |

D The CoxIngersollRoss Model | 141 |

E The Affine SingleFactor Models | 142 |

F TermStructure Derivatives | 144 |

G The Fundamental Solution | 146 |

H Multifactor Models | 148 |

I Affine TermStructure Models | 149 |

J The HJM Model of Forward Rates | 151 |

K Markovian Yield Curves and SPDEs | 154 |

Exercises | 155 |

Notes | 161 |

Derivative Pricing | 167 |

Exercises | 191 |

Notes | 196 |

Portfolio and Consumption Choice | 203 |

B Mertons Problem | 206 |

C Solution to Mertons Problem | 209 |

D The InfiniteHorizon Case | 213 |

E The Martingale Formulation | 214 |

F Martingale Solution | 217 |

G A Generalization | 220 |

H The UtilityGradient Approach | 221 |

Exercises | 224 |

Notes | 232 |

Equilibrium | 235 |

B SecuritySpot Market Equilibrium | 236 |

C ArrowDebreu Equilibrium | 237 |

D Implementing ArrowDebreu Equilibrium | 238 |

E Real Security Prices | 240 |

F Optimality with Additive Utility | 241 |

G Equilibrium with Additive Utility | 243 |

H The ConsumptionBased CAPM | 245 |

I The CIR Term Structure | 246 |

J The CCAPM in Incomplete Markets | 249 |

Exercises | 251 |

Notes | 255 |

Corporate Securities | 259 |

B Endogenous Default Timing | 262 |

Brownian Dividend Growth | 264 |

D Taxes and Bankruptcy Costs | 268 |

E Endogenous Capital Structure | 269 |

F Technology Choice | 271 |

G Other Market Imperfections | 272 |

H IntensityBased Modeling of Default | 274 |

I RiskNeutral Intensity Process | 277 |

J ZeroRecovery Bond Pricing | 278 |

K Pricing with Recovery at Default | 280 |

L DefaultAdjusted Short Rate | 281 |

Exercises | 282 |

Notes | 288 |

Numerical Methods | 293 |

B Binomial to BlackScholes | 294 |

C Binomial Convergence for Unbounded Derivative Payoffs | 297 |

E Monte Carlo Simulation | 299 |

F Efficient SDE Simulation | 300 |

G Applying FeynmanKac | 302 |

I TermStructure Example | 306 |

J FiniteDifference Algorithms with Early Exercise Options | 309 |

K The Numerical Solution of State Prices | 310 |

L Numerical Solution of the Pricing SemiGroup | 313 |

M Fitting the Initial Term Structure | 314 |

Exercises | 316 |

Notes | 317 |

APPENDIXES | 321 |

FiniteState Probability | 323 |

Separating Hyperplanes and Optimality | 326 |

Probability | 329 |

Stochastic Integration | 334 |

SDE PDE and FeynmanKac | 340 |

Itos Formula with Jumps | 347 |

Utility Gradients | 351 |

Itos Formula for Complex Functions | 355 |

Counting Processes | 357 |

FiniteDifference Code | 363 |

Bibliography | 373 |

Symbol Glossary | 445 |

Author Index | 447 |

457 | |