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| List of illustrations | |
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| Preface | |
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| Options | |
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| What are options? | |
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| Why do we study options? | |
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| How are options traded? | |
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| Typical option prices | |
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| Other financial derivatives | |
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| Notes and references | |
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| Program of Chapter 1 and walkthrough | |
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| Option valuation preliminaries | |
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| Motivation | |
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| Interest rates | |
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| Short selling | |
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| Arbitrage | |
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| Put-call parity | |
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| Upper and lower bounds on option values | |
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| Notes and references | |
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| Program of Chapter 2 and walkthrough | |
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| Random variables | |
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| Motivation | |
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| Random variables, probability and mean | |
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| Independence | |
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| Variance | |
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| Normal distribution | |
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| Central Limit Theorem | |
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| Notes and references | |
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| Program of Chapter 3 and walkthrough | |
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| Computer simulation | |
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| Motivation | |
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| Pseudo-random numbers | |
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| Statistical tests | |
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| Notes and references | |
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| Program of Chapter 4 and walkthrough | |
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| Asset price movement | |
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| Motivation | |
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| Efficient market hypothesis | |
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| Asset price data | |
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| Assumptions | |
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| Notes and references | |
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| Program of Chapter 5 and walkthrough | |
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| Asset price model: Part I | |
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| Motivation | |
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| Discrete asset model | |
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| Continuous asset model | |
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| Lognormal distribution | |
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| Features of the asset model | |
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| Notes and references | |
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| Program of Chapter 6 and walkthrough | |
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| Asset price model: Part II | |
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| Computing asset paths | |
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| Timescale invariance | |
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| Sum-of-square returns | |
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| Notes and references | |
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| Program of Chapter 7 and walkthrough | |
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| Black-Scholes PDE and formulas | |
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| Motivation | |
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| Sum-of-square increments for asset price | |
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| Hedging | |
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| Black-Scholes PDE | |
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| Black-Scholes formulas | |
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| Notes and references | |
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| Program of Chapter 8 and walkthrough | |
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| More on hedging | |
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| Motivation | |
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| Discrete hedging | |
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| Delta at expiry | |
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| Large-scale test | |
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| Long-Term Capital Management | |
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| Notes | |
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| Program of Chapter 9 and walkthrough | |
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| The Greeks | |
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| Motivation | |
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| The Greeks | |
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| Interpreting the Greeks | |
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| Black-Scholes PDE solution | |
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| Notes and references | |
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| Program of Chapter 10 and walkthrough | |
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| More on the Black-Scholes formulas | |
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| Motivation | |
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| Where is [mu]? | |
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| Time dependency | |
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| The big picture | |
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| Change of variables | |
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| Notes and references | |
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| Program of Chapter 11 and walkthrough | |
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| Risk neutrality | |
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| Motivation | |
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| Expected payoff | |
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| Risk neutrality | |
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| Notes and references | |
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| Program of Chapter 12 and walkthrough | |
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| Solving a nonlinear equation | |
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| Motivation | |
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| General problem | |
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| Bisection | |
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| Newton | |
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| Further practical issues | |
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| Notes and references | |
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| Program of Chapter 13 and walkthrough | |
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| Implied volatility | |
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| Motivation | |
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| Implied volatility | |
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| Option value as a function of volatility | |
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| Bisection and Newton | |
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| Implied volatility with real data | |
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| Notes and references | |
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| Program of Chapter 14 and walkthrough | |
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| Monte Carlo method | |
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| Motivation | |
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| Monte Carlo | |
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| Monte Carlo for option valuation | |
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| Monte Carlo for Greeks | |
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| Notes and references | |
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| Program of Chapter 15 and walkthrough | |
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| Binomial method | |
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| Motivation | |
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| Method | |
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| Deriving the parameters | |
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| Binomial method in practice | |
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| Notes and references | |
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| Program of Chapter 16 and walkthrough | |
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| Cash-or-nothing options | |
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| Motivation | |
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| Cash-or-nothing options | |
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| Black-Scholes for cash-or-nothing options | |
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| Delta behaviour | |
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| Risk neutrality for cash-or-nothing options | |
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| Notes and references | |
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| Program of Chapter 17 and walkthrough | |
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| American options | |
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| Motivation | |
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| American call and put | |
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| Black-Scholes for American options | |
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| Binomial method for an American put | |
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| Optimal exercise boundary | |
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| Monte Carlo for an American put | |
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| Notes and references | |
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| Program of Chapter 18 and walkthrough | |
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| Exotic options | |
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| Motivation | |
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| Barrier options | |
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| Lookback options | |
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| Asian options | |
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| Bermudan and shout options | |
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| Monte Carlo and binomial for exotics | |
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| Notes and references | |
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| Program of Chapter 19 and walkthrough | |
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| Historical volatility | |
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| Motivation | |
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| Monte Carlo-type estimates | |
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| Accuracy of the sample variance estimate | |
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| Maximum likelihood estimate | |
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| Other volatility estimates | |
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| Example with real data | |
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| Notes and references | |
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| Program of Chapter 20 and walkthrough | |
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| Monte Carlo Part II: variance reduction by antithetic variates | |
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| Motivation | |
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| The big picture | |
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| Dependence | |
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| Antithetic variates: uniform example | |
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| Analysis of the uniform case | |
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| Normal case | |
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| Multivariate case | |
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| Antithetic variates in option valuation | |
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| Notes and references | |
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| Program of Chapter 21 and walkthrough | |
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| Monte Carlo Part III: variance reduction by control variates | |
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| Motivation | |
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| Control variates | |
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| Control variates in option valuation | |
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| Notes and references | |
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| Program of Chapter 22 and walkthrough | |
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| Finite difference methods | |
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| Motivation | |
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| Finite difference operators | |
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| Heat equation | |
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| Discretization | |
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| FTCS and BTCS | |
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| Local accuracy | |
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| Von Neumann stability and convergence | |
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| Crank-Nicolson | |
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| Notes and references | |
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| Program of Chapter 23 and walkthrough | |
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| Finite difference methods for the Black-Scholes PDE | |
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| Motivation | |
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| FTCS, BTCS and Crank-Nicolson for Black-Scholes | |
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| Down-and-out call example | |
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| Binomial method as finite differences | |
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| Notes and references | |
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| Program of Chapter 24 and walkthrough | |
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| References | |
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| Index | |