Dynamic Asset Pricing Theory

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Princeton University Press, Jan 27, 2010 - Business & Economics - 488 pages
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This is a thoroughly updated edition of Dynamic 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 Theory remains at the head of the field.

 

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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

B Security Markets
22
D Individual Agent Optimality
24
E Equilibrium and Pareto Optimality
26
F Equilibrium Asset Pricing
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
Subject Index
457
Copyright

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About the author (2010)

Darrell Duffie is the Dean Witter Distinguished Professor of Finance at Stanford University's Graduate School of Business. His books include "How Big Banks Fail and What to Do about It" and "Dynamic Asset Pricing Theory" (both Princeton).

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