1 Introduction; 1.1 Problem Formulation; 2 The Binomial Model; 2.1 The One Period Model; 2.1.1 Model Description; 2.1.2 Portfolios and Arbitrage; 2.1.3 Contingent Claims; 2.1.4 Risk Neutral Valuation; 2.2 The Multiperiod Model; 2.2.1 Portfolios and Arbitrage; 2.2.2 Contingent Claims; 2.3 Exercises; 2.4 Notes; 3 A More General One Period Model; 3.1 The Model; 3.2 Absence of Arbitrage; 3.3 Martingale Pricing; 3.4 Completeness; 3.5 Stochastic Discount Factors; 3.6 Exercises; 4 Stochastic Integrals; 4.1 Introduction; 4.2 Information; 4.3 Stochastic Integrals; 4.4 Martingales
4.5 Stochastic Calculus and the Itô Formula4.6 Examples; 4.7 The Multidimensional Itô Formula; 4.8 Correlated Wiener Processes; 4.9 Exercises; 4.10 Notes; 5 Differential Equations; 5.1 Stochastic Differential Equations; 5.2 Geometric Brownian Motion; 5.3 The Linear SDE; 5.4 The Infinitesimal Operator; 5.5 Partial Differential Equations; 5.6 The Kolmogorov Equations; 5.7 Exercises; 5.8 Notes; 6 Portfolio Dynamics; 6.1 Introduction; 6.2 Self-financing Portfolios; 6.3 Dividends; 6.4 Exercise; 7 Arbitrage Pricing; 7.1 Introduction; 7.2 Contingent Claims and Arbitrage
7.3 The Black-Scholes Equation7.4 Risk Neutral Valuation; 7.5 The Black-Scholes Formula; 7.6 Options on Futures; 7.6.1 Forward Contracts; 7.6.2 Futures Contracts and the Black Formula; 7.7 Volatility; 7.7.1 Historic Volatility; 7.7.2 Implied Volatility; 7.8 American options; 7.9 Exercises; 7.10 Notes; 8 Completeness and Hedging; 8.1 Introduction; 8.2 Completeness in the Black-Scholes Model; 8.3 Completeness-Absence of Arbitrage; 8.4 Exercises; 8.5 Notes; 9 Parity Relations and Delta Hedging; 9.1 Parity Relations; 9.2 The Greeks; 9.3 Delta and Gamma Hedging; 9.4 Exercises
10 The Martingale Approach to Arbitrage Theory*10.1 The Case with Zero Interest Rate; 10.2 Absence of Arbitrage; 10.2.1 A Rough Sketch of the Proof; 10.2.2 Precise Results; 10.3 The General Case; 10.4 Completeness; 10.5 Martingale Pricing; 10.6 Stochastic Discount Factors; 10.7 Summary for the Working Economist; 10.8 Notes; 11 The Mathematics of the Martingale Approach*; 11.1 Stochastic Integral Representations; 11.2 The Girsanov Theorem: Heuristics; 11.3 The Girsanov Theorem; 11.4 The Converse of the Girsanov Theorem; 11.5 Girsanov Transformations and Stochastic Differentials
11.6 Maximum Likelihood Estimation11.7 Exercises; 11.8 Notes; 12 Black-Scholes from a Martingale Point of View*; 12.1 Absence of Arbitrage; 12.2 Pricing; 12.3 Completeness; 13 Multidimensional Models: Classical Approach; 13.1 Introduction; 13.2 Pricing; 13.3 Risk Neutral Valuation; 13.4 Reducing the State Space; 13.5 Hedging; 13.6 Exercises; 14 Multidimensional Models: Martingale Approach*; 14.1 Absence of Arbitrage; 14.2 Completeness; 14.3 Hedging; 14.4 Pricing; 14.5 Markovian Models and PDEs; 14.6 Market Prices of Risk; 14.7 Stochastic Discount Factors; 14.8 The Hansen-Jagannathan Bounds
Summary
The second edition of this introduction to the classical underpinnings of the mathematics behind finance continues to combine sound mathematical principles with economic applications
Bibliography
Includes bibliographical references (pages 453-460) and index
