The Black-Scholes Model.

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Master the essential mathematical tools required for option pricing within the context of a specific, yet fundamental, pricing model.

Cover; The Black-Scholes Model; Title; Copyright; Contents; Preface; 1 Introduction; 1.1 Asset dynamics; Model parameters; 1.2 Methods of option pricing; Risk-neutral probability approach; The PDE approach; 2 Strategies and risk-neutral probability; 2.1 Finding the risk-neutral probability; Removing the drift; Girsanov theorem -- simple version; 2.2 Self-financing strategies; 2.3 The No Arbitrage Principle; 2.4 Admissible strategies; 2.5 Proofs; 3 Option pricing and hedging; 3.1 Martingale representation theorem; 3.2 Completeness of the model; 3.3 Derivative pricing.

General derivative securitiesPut options; Call options; 3.4 The Black-Scholes PDE; From Black-Scholes PDE to option price; The replicating strategy; 3.5 The Greeks; 3.6 Risk and return; 3.7 Proofs; 4 Extensions and applications; 4.1 Options on foreign currency; Dividend paying stock; 4.2 Structural model of credit risk; 4.3 Compound options; 4.4 American call options; 4.5 Variable coefficients; 4.6 Growth optimal portfolios; 5 Path-dependent options; 5.1 Barrier options; 5.2 Distribution of the maximum; 5.3 Pricing barrier and lookback options; Hedging; Lookback option; 5.4 Asian options.

Continuous geometric averageDiscrete geometric average; 6 General models; 6.1 Two assets; The market; Strategies and risk-neutral probabilities; Two stocks, one Wiener process; One stock, two Wiener processes; 6.2 Many assets; 6.3 Ito formula; 6.4 Levy's Theorem; 6.5 Girsanov Theorem; 6.6 Applications; Index.

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