Dynamic Asset Pricing Theory

by Duffie, Darrell

• ISBN13: 9780691090221
• ISBN10: 069109022X
• Edition: 3rd
• Format: Hardcover
• Copyright: 2001-10-01
• 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.

Author Biography

Darrell Duffie is the James Irvin Miller Professor of Finance at the Graduate School of Business, Stanford University. He teaches and does research in the area of asset valuation, risk management, credit risk modeling, and fixed-income and equity markets

Table of Contents

Preface	xiii
PART I DISCRETE-TIME MODELS	1	(80)
Introduction to State Pricing	3	(18)
Arbitrage and State Prices	3	(1)
Risk-Neutral Probabilities	4	(1)
Optimality and Asset Pricing	5	(3)
Efficiency and Complete Markets	8	(1)
Optimality and Representative Agents	8	(3)
State-Price Beta Models	11	(10)
Exercises	12	(5)
Notes	17	(4)
The Basic Multiperiod Model	21	(28)
Uncertainty	21	(1)
Security Markets	22	(1)
Arbitrage, State Prices, and Martingales	22	(2)
Individual Agent Optimality	24	(2)
Equilibrium and Pareto Optimality	26	(1)
Equilibrium Asset Pricing	27	(1)
Arbitrage and Martingale Measures	28	(2)
Valuation of Redundant Securities	30	(1)
American Exercise Policies and Valuation	31	(4)
Is Early Exercise Optimal?	35	(14)
Exercises	37	(8)
Notes	45	(4)
The Dynamic Programming Approach	49	(16)
The Bellman Approach	49	(1)
First-Order Bellman Conditions	50	(1)
Markov Uncertainty	51	(1)
Markov Asset Pricing	52	(1)
Security Pricing by Markov Control	52	(3)
Markov Arbitrage-Free Valuation	55	(1)
Early Exercise and Optimal Stopping	56	(9)
Exercises	58	(5)
Notes	63	(2)
The Infinite-Horizon Setting	65	(16)
Markov Dynamic Programming	65	(4)
Dynamic Programming and Equilibrium	69	(1)
Arbitrage and State Prices	70	(1)
Optimality and State Prices	71	(2)
Method-of-Moments Estimation	73	(8)
Exercises	76	(2)
Notes	78	(3)
PART II CONTINUOUS-TIME MODELS	81	(240)
The Black-Scholes Model	83	(18)
Trading Gains for Brownian Prices	83	(2)
Martingale Trading Gains	85	(1)
Ito Prices and Gains	86	(1)
Ito's Formula	87	(1)
The Black-Scholes Option-Pricing Formula	88	(2)
Black-Scholes Formula: First Try	90	(2)
The PDE for Arbitrage-Free Prices	92	(1)
The Feynman-Kac Solution	93	(1)
The Multidimensional Case	94	(7)
Exercises	97	(3)
Notes	100	(1)
State Prices and Equivalent Martingale Measures	101	(34)
Arbitrage	101	(1)
Numeraire Invariance	102	(1)
State Prices and Doubling Strategies	103	(3)
Expected Rates of Return	106	(2)
Equivalent Martingale Measures	108	(2)
State Prices and Martingale Measures	110	(1)
Girsanov and Market Prices of Risk	111	(4)
Black-Scholes Again	115	(1)
Complete Markets	116	(3)
Redundant Security Pricing	119	(1)
Martingale Measures from No Arbitrage	120	(3)
Arbitrage Pricing with Dividends	123	(2)
Lumpy Dividends and Term Structures	125	(2)
Martingale Measures, Infinite Horizon	127	(8)
Exercises	128	(3)
Notes	131	(4)
Term-Structure Models	135	(32)
The Term Structure	136	(1)
One-Factor Term-Structure Models	137	(2)
The Gaussian Single-Factor Models	139	(2)
The Cox-Ingersoll-Ross Models	141	(1)
The Affine Single-Factor Models	142	(2)
Term-Structure Derivatives	144	(2)
The Fundamental Solution	146	(2)
Multifactor Models	148	(1)
Affine Term-Structure Models	149	(2)
The HJM Model of Forward Rates	151	(3)
Markovian Yield Curves and SPDEs	154	(13)
Exercises	155	(6)
Notes	161	(6)
Derivative Pricing	167	(36)
Martingale Measures in a Black Box	167	(2)
Forward Prices	169	(2)
Futures and Continuous Resettlement	171	(1)
Arbitrage-Free Futures Prices	172	(2)
Stochastic Volatility	174	(4)
Option Valuation by Transform Analysis	178	(4)
American Security Valuation	182	(4)
American Exercise Boundaries	186	(3)
Lookback Options	189	(14)
Exercises	191	(5)
Notes	196	(7)
Portfolio and Consumption Choice	203	(32)
Stochastic Control	203	(3)
Merton's Problem	206	(3)
Solution to Merton's Problem	209	(4)
The Infinite-Horizon Case	213	(1)
The Martingale Formulation	214	(3)
Martingale Solution	217	(3)
A Generalization	220	(1)
The Utility-Gradient Approach	221	(14)
Exercises	224	(8)
Notes	232	(3)
Equilibrium	235	(24)
The Primitives	235	(1)
Security-Spot Market Equilibrium	236	(1)
Arrow-Debreu Equilibrium	237	(1)
Implementing Arrow-Debreu Equilibrium	238	(2)
Real Security Prices	240	(1)
Optimality with Additive Utility	241	(2)
Equilibrium with Additive Utility	243	(2)
The Consumption-Based CAPM	245	(1)
The CIR Term Structure	246	(3)
The CCAPM in Incomplete Markets	249	(10)
Exercises	251	(4)
Notes	255	(4)
Corporate Securities	259	(34)
The Black-Scholes-Merton Model	259	(3)
Endogenous Default Timing	262	(2)
Example: Brownian Dividend Growth	264	(4)
Taxes and Bankruptcy Costs	268	(1)
Endogenous Capital Structure	269	(2)
Technology Choice	271	(1)
Other Market Imperfections	272	(2)
Intensity-Based Modeling of Default	274	(3)
Risk-Neutral Intensity Process	277	(1)
Zero-Recovery Bond Pricing	278	(2)
Pricing with Recovery at Default	280	(1)
Default-Adjusted Short Rate	281	(12)
Exercises	282	(6)
Notes	288	(5)
Numerical Methods	293	(28)
Central Limit Theorems	293	(1)
Binomial to Black-Scholes	294	(3)
Binomial Convergence for Unbounded Derivative Payoffs	297	(1)
Discretization of Asset Price Processes	297	(2)
Monte Carlo Simulation	299	(1)
Efficient SDE Simulation	300	(2)
Applying Feynman-Kac	302	(1)
Finite-Difference Methods	302	(4)
Term-Structure Example	306	(3)
Finite-Difference Algorithms with Early Exercise Options	309	(1)
The Numerical Solution of State Prices	310	(3)
Numerical Solution of the Pricing Semi-Group	313	(1)
Fitting the Initial Term Structure	314	(7)
Exercises	316	(1)
Notes	317	(4)
APPENDIXES	321	(52)
A Finite-State Probability	323	(3)
B Separating Hyperplanes and Optimality	326	(3)
CProbability	329	(5)
D Stochastic Integration	334	(6)
E SDE, PDE, and Feynman-Kac	340	(7)
F Ito's Formula with Jumps	347	(4)
G Utility Gradients	351	(4)
H Ito's Formula for Complex Functions	355	(2)
I Counting Processes	357	(6)
J Finite-Difference Code	363	(10)
Bibliography	373	(72)
Symbol Glossary	445	(2)
Author Index	447	(10)
Subject Index	457