The Black-Scholes 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 securities -- Put 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 average -- Discrete 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.