PART Ⅰ DISCRETE- TIME MODELS 1
1 Introduction to State Pricing 3
A Arbitrage and State Prices 3
B Risk-Neutral Probabilities 4
C Optimality and Asset Pricing 5
D Efficiency and Complete Markets 8
E Optimality and Representative Agents 8
F State-Price Beta Models 11
Exercises 12
Notes 17
2 The Basic Multiperiod Model 21
A Uncertainty 21
B Security Markets 22
C Arbitrage,State Prices,and Martingales 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
3 The Dynamic Programming Approach 49
A The Bellman Approach 49
B First-Order Bellman Conditions 50
C Markov Uncertainty 51
D Markov Asset Pricing 52
E Security Pricing by Markov Control 52
F Markov Arbitrage-Free Valuation 55
G Early Exercise and Optimal Stopping 56
Exercises 58
Notes 63
4 The Infinite-Horizon Setting 65
A Markov Dynamic Programming 65
B Dynamic Programming and Equilibrium 69
C Arbitrage and State Prices 70
D Optimality and State Prices 71
E Method-of-Moments Estimation 73
Exercises 76
Notes 78
PART Ⅱ CONTINUOUS-TIME MODELS 81
5 The Black-Scholes Model 83
A Trading Gains for Brownian Prices 83
B Martingale Trading Gains 85
C Ito Prices and Gains 86
D Ito's Formula 87
E The Black-Scholes Option-Pricing Formula 88
F Black-Scholes Formula:First Try 90
G The PDE for Arbitrage-Free Prices 92
H The Feynman-Kac Solution 93
I The Multidimensional Case 94
Exercises 97
Notes 100
6 State Prices and Equivalent Martingale Measures 101
A Arbitrage 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 Black-Scholes 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
7 Term-Structure Models 135
A The Term Structure 136
B One-Factor Term-Structure Models 137
C The Gaussian Single-Factor Models 139
D The Cox-Ingersoll-Ross Model 141
E The Affine Single-Factor Models 142
F Term-Structure Derivatives 144
G The Fundamental Solution 146
H Multifactor Models 148
I Affine Term-Structure Models 149
J The HJM Model of Forward Rates 151
K Markovian Yield Curves and SPDEs 154
Exercises 155
Notes 161
8 Derivative Pricing 167
A Martingale Measures in a Black Box 167
B Forward Prices 169
C Futures and Continuous Resettlement 171
D Arbitrage-Free 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
Exercises 191
Notes 196
9 Portfolio and Consumption Choice 203
A Stochastic Control 203
B Merton's Problem 206
C Solution to Merton's Problem 209
D The Infinite-Horizon Case 213
E The Martingale Formulation 214
F Martingale Solution 217
G A Generalization 220
H The Utility-Gradient Approach 221
Exercises 224
Notes 232
10 Equilibrium 235
A The Primitives 235
B Security-Spot Market Equilibrium 236
C Arrow-Debreu Equilibrium 237
D Implementing Arrow-Debreu Equilibrium 238
E Real Security Prices 240
F Optimality with Additive Utility 241
G Equilibrium with Additive Utility 243
H The Consumption-Based CAPM 245
I The CIR Term Structure 246
J The CCAPM in Incomplete Markets 249
Exercises 251
Notes 255
11 Corporate Securities 259
A The Black-Scholes-Merton Model 259
B Endogenous Default Timing 262
C Example: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 Intensity-Based Modeling of Default 274
I Risk-Neutral Intensity Process 277
J Zero-Recovery Bond Pricing 278
K Pricing with Recovery at Default 280
L Default-Adjusted Short Rate 281
Exercises 282
Notes 288
12 Numerical Methods 293
A Central Limit Theorems 293
B Binomial to Black-Scholes 294
C Binomial Convergence for Unbounded Derivative Payoffs 297
D Discretization of Asset Price Processes 297
E Monte Carlo Simulation 299
F Efficient SDE Simulation 300
G Applying Feynman-Kac 302
H Finite-Difference Methods 302
I Term-Structure Example 306
J Finite-Difference Algorithms with Early Exercise Options 309
K The Numerical Solution of State Prices 310
L Numerical Solution of the Pricing Semi-Group 313
M Fitting the Initial Term Structure 314
Exercises 316
Notes 317
APPENDIXES 321
A Finite-State Probability 323
B Separating Hyperplanes and Optimality 326
C Probability 329
D Stochastic Integration 334
E SDE,PDE,and Feynman-Kac 340
F Ito's Formula with Jumps 347
G Utility Gradients 351
H Ito's Formula for Complex Functions 355
I Counting Processes 357
J Finite-Difference Code 363
Bibliography 373
Symbol Glossary 445
Author Index 447
Subject Index 457