Dynamic Asset Pricing Theory

by Duffie, Darrell

• ISBN13: 9781400829200
• ISBN10: 1400829208
• Edition: 3rd
• Copyright: 2008-06-01
• Publisher: Princeton Univ Pr

Summary

This is a thoroughly updated edition ofDynamic Asset Pricing Theory, the standard text for doctoral students and researchers on the theory of asset pricing and portfolio selection in multiperiod settings under uncertainty. The asset pricing results are based on the three increasingly restrictive assumptions: absence of arbitrage, single-agent optimality, and equilibrium. These results are unified with two key concepts, state prices and martingales. Technicalities are given relatively little emphasis, so as to draw connections between these concepts and to make plain the similarities between discrete and continuous-time models. 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,Dynamic Asset Pricing Theoryremains at the head of the field.

Table of Contents

Preface	p. xiii
Discrete-Time Models	p. 1
Introduction to State Pricing	p. 3
Arbitrage and State Prices	p. 3
Risk-Neutral Probabilities	p. 4
Optimality and Asset Pricing	p. 5
Efficiency and Complete Markets	p. 8
Optimality and Representative Agents	p. 8
State-Price Beta Models	p. 11
Exercises	p. 12
Notes	p. 17
The Basic Multiperiod Model	p. 21
Uncertainty 21 B Security Markets	p. 22
Arbitrage, State Prices, and Martingales	p. 22
Individual Agent Optimality	p. 24
Equilibrium and Pareto Optimality	p. 26
Equilibrium Asset Pricing	p. 27
Arbitrage and Martingale Measures	p. 28
Valuation of Redundant Securities	p. 30
American Exercise Policies and Valuation	p. 31
Is Early Exercise Optimal?	p. 35
Exercises	p. 37
Notes	p. 45
The Dynamic Programming Approach	p. 49
The Bellman Approach	p. 49
First-Order Bellman Conditions	p. 50
Markov Uncertainty .51
Markov Asset Pricing	p. 52
Security Pricing by Markov Control	p. 52
Markov Arbitrage-Free Valuation	p. 55
Early Exercise and Optimal Stopping	p. 56
Exercises	p. 58
Notes	p. 63
The Infinite-Horizon Setting	p. 65
Markov Dynamic Programming .65
Dynamic Programming and Equilibrium.69
Arbitrage and State Prices	p. 70
Optimality and State Prices.71
Method-of-Moments Estimation .73
Exercises	p. 76
Notes	p. 78
Continuous-Time Models	p. 81
The Black-Scholes Model	p. 83
Trading Gains for Brownian Prices	p. 83
Martingale Trading Gains	p. 85
Ito Prices and Gains	p. 86
Ito's Formula	p. 87
The Black-Scholes Option-Pricing Formula	p. 88
Black-Scholes Formula: First Try	p. 90
The PDE for Arbitrage-Free Prices	p. 92
The Feynman-Kac Solution	p. 93
The Multidimensional Case	p. 94
Exercises	p. 97
Notes	p. 100
State Prices and Equivalent Martingale Measures	p. 101
Arbitrage	p. 101
Numeraire Invariance	p. 102
State Prices and Doubling Strategies	p. 103
Expected Rates of Return	p. 106
Equivalent Martingale Measures	p. 108
State Prices and Martingale Measures	p. 110
Girsanov and Market Prices of Risk	p. 111
Black-Scholes Again	p. 115
Complete Markets	p. 116
Redundant Security Pricing	p. 119
Martingale Measures from No Arbitrage	p. 120
Arbitrage Pricing with Dividends	p. 123
Lumpy Dividends and Term Structures	p. 125
Martingale Measures, Infinite Horizon	p. 127
Exercises	p. 128
Notes	p. 131
Term-Structure Models	p. 135
The Term Structure	p. 136
One-Factor Term-Structure Models	p. 137
The Gaussian Single-Factor Models	p. 139
The Cox-Ingersoll-Ross Model	p. 141
The Affine Single-Factor Models	p. 142
Term-Structure Derivatives	p. 144
The Fundamental Solution	p. 146
Multifactor Models	p. 148
Affine Term-Structure Models	p. 149
The HJM Model of Forward Rates	p. 151
Markovian Yield Curves and SPDEs	p. 154
Exercises	p. 155
Notes	p. 161
Derivative Pricing	p. 167
Martingale Measures in a Black Box	p. 167
Forward Prices	p. 169
Futures and Continuous Resettlement	p. 171
Arbitrage-Free Futures Prices	p. 172
Stochastic Volatility	p. 174
Option Valuation by Transform Analysis	p. 178
American Security Valuation	p. 182
American Exercise Boundaries	p. 186
Lookback Options	p. 189
Exercises	p. 191
Notes	p. 196
Portfolio and Consumption Choice	p. 203
Stochastic Control	p. 203
Merton's Problem	p. 206
Solution to Merton's Problem	p. 209
The Infinite-Horizon Case	p. 213
The Martingale Formulation	p. 214
Martingale Solution	p. 217
A Generalization	p. 220
The Utility-Gradient Approach	p. 221
Exercises	p. 224
Notes	p. 232
Equilibrium	p. 235
The Primitives	p. 235
Security-Spot Market Equilibrium	p. 236
Arrow-Debreu Equilibrium	p. 237
Implementing Arrow-Debreu Equilibrium	p. 238
Real Security Prices	p. 240
Optimality with Additive Utility	p. 241
Equilibrium with Additive Utility	p. 243
The Consumption-Based CAPM	p. 245
The CIR Term Structure	p. 246
The CCAPM in Incomplete Markets	p. 249
Exercises	p. 251
Notes	p. 255
Corporate Securities	p. 259
The Black-Scholes-Merton Model	p. 259
Endogenous Default Timing	p. 262
Example: Brownian Dividend Growth	p. 264
Taxes and Bankruptcy Costs	p. 268
Endogenous Capital Structure	p. 269
Technology Choice	p. 271
Other Market Imperfections	p. 272
Intensity-Based Modeling of Default	p. 274
Risk-Neutral Intensity Process	p. 277
Zero-Recovery Bond Pricing	p. 278
Pricing with Recovery at Default	p. 280
Default-Adjusted Short Rate	p. 281
Exercises	p. 282
Notes	p. 288
Numerical Methods	p. 293
Central Limit Theorems	p. 293
Binomial to Black-Scholes	p. 294
Binomial Convergence for Unbounded Derivative Payoffs	p. 297
Discretization of Asset Price Processes	p. 297
Monte Carlo Simulation	p. 299
Efficient SDE Simulation	p. 300
Applying Feynman-Kac	p. 302
Finite-Difference Methods	p. 302
Term-Structure Example	p. 306
Finite-Difference Algorithms with Early Exercise Options	p. 309
The Numerical Solution of State Prices	p. 310
Numerical Solution of the Pricing Semi-Group	p. 313
Fitting the Initial Term Structure	p. 314
Exercises	p. 316
Notes	p. 317
Appendixes	p. 321
Finite-State Probability	p. 323
Separating Hyperplanes and Optimality	p. 326
Probability	p. 329
Stochastic Integration	p. 334
SDE, PDE, and Feynman-Kac	p. 340
Ito's Formula with jumps	p. 347
Utility Gradients	p. 351
Ito's Formula for Complex Functions	p. 355
Counting Processes	p. 357
Finite-Difference Code	p. 363
Bibliography	p. 373
Symbol Glossary	p. 445
Author Index	p. 447
Subject Index	p. 457
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