Frontmatter Page ix Monday, March 8, 2004 10:06 AM
Contents ixCHAPTER 14
Arbitrage Pricing: Finite-State Models 393
The Arbitrage Principle 393
Arbitrage Pricing in a One-Period Setting 395
State Prices 397
Risk-Neutral Probabilities 398
Complete Markets 399
Arbitrage Pricing in a Multiperiod Finite-State Setting 402
Propagation of Information 402
Trading Strategies 403
State-Price Deflator 404
Pricing Relationships 405
Equivalent Martingale Measures 414
Risk-Neutral Probabilities 416
Path Dependence and Markov Models 423
The Binomial Model 423
Risk-Neutral Probabilities for the Binomial Model 426
Valuation of European Simple Derivatives 427
Valuation of American Options 429
Arbitrage Pricing in a Discrete-Time, Continuous-State Setting 430
APT Models 435
Testing APT 436
Summary 439
CHAPTER 15
Arbitrage Pricing: Continuous-State, Continuous-Time Models 441
The Arbitrage Principle in Continuous Time 441
Trading Strategies and Trading Gains 443
Arbitrage Pricing in Continuous-State, Continuous-Time 445
Option Pricing 447
Stock Price Processes 447
Hedging 448
The Black-Scholes Option Pricing Formula 449
Generalizing the Pricing of European Options 452
State-Price Deflators 454
Equivalent Martingale Measures 457
Equivalent Martingale Measures and Girsanov’s Theorem 459
The Diffusion Invariance Principle 461
Application of Girsanov’s Theorem to Black-Scholes
Option Pricing Formula 462
Equivalent Martingale Measures and Complete Markets 463
Equivalent Martingale Measures and State Prices 464
Arbitrage Pricing with a Payoff Rate 466
Implications of the Absence of Arbitrage 467
Working with Equivalent Martingale Measures 468
Summary 468