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| Introduction and Preface | |
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| Probability | |
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| Probabilities and Events | |
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| Conditional Probability | |
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| Random Variables and Expected Values | |
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| Covariance and Correlation | |
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| Conditional Expectation | |
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| Exercises | |
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| Normal Random Variables | |
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| Continuous Random Variables | |
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| Normal Random Variables | |
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| Properties of Normal Random Variables | |
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| The Central Limit Theorem | |
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| Exercises | |
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| Brownian Motion and Geometric Brownian Motion | |
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| Brownian Motion | |
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| Brownian Motion as a Limit of Simpler Models | |
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| Geometric Brownian Motion | |
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| Geometric Brownian Motion as a Limit of Simpler Models | |
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| *The Maximum Variable | |
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| The Cameron-Martin Theorem | |
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| Exercises | |
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| Interest Rates and Present Value Analysis | |
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| Interest Rates | |
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| Present Value Analysis | |
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| Rate of Return | |
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| Continuously Varying Interest Rates | |
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| Exercises | |
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| Pricing Contracts via Arbitrage | |
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| An Example in Options Pricing | |
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| Other Examples of Pricing via Arbitrage | |
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| Exercises | |
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| The Arbitrage Theorem | |
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| The Arbitrage Theorem | |
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| The Multiperiod Binomial Model | |
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| Proof of the Arbitrage Theorem | |
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| Exercises | |
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| The Black-Scholes Formula | |
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| Introduction | |
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| The Black-Scholes Formula | |
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| Properties of the Black-Scholes Option Cost | |
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| The Delta Hedging Arbitrage Strategy | |
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| Some Derivations | |
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| The Black-Scholes Formula | |
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| The Partial Derivatives | |
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| European Put Options | |
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| Exercises | |
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| Additional Results on Options | |
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| Introduction | |
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| Call Options on Dividend-Paying Securities | |
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| The Dividend for Each Share of the Security Is Paid Continuously in Time at a Rate Equal to a Fixed Fraction f of the Price of the Security | |
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| For Each Share Owned, a Single Payment of fS(t<sub>d</sub>) Is Made at Time t<sub>d</sub> | |
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| For Each Share Owned, a Fixed Amount D Is to Be Paid at Time t<sub>d</sub> | |
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| Pricing American Put Options | |
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| Adding Jumps to Geometric Brownian Motion | |
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| When the Jump Distribution Is Lognormal | |
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| When the Jump Distribution Is General | |
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| Estimating the Volatility Parameter | |
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| Estimating a Population Mean and Variance | |
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| The Standard Estimator of Volatility | |
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| Using Opening and Closing Data | |
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| Using Opening, Closing, and High-Low Data | |
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| Some Comments | |
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| When the Option Cost Differs from the Black-Scholes Formula | |
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| When the Interest Rate Changes | |
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| Final Comments | |
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| Appendix | |
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| Exercises | |
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| Valuing by Expected Utility | |
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| Limitations of Arbitrage Pricing | |
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| Valuing Investments by Expected Utility | |
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| The Portfolio Selection Problem | |
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| Estimating Covariances | |
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| Value at Risk and Conditional Value at Risk | |
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| The Capital Assets Pricing Model | |
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| Rates of Return: Single-Period and Geometric Brownian Motion | |
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| Exercises | |
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| Stochastic Order Relations | |
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| First-Order Stochastic Dominance | |
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| Using Coupling to Show Stochastic Dominance | |
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| Likelihood Ratio Ordering | |
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| A Single-Period Investment Problem | |
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| Second-Order Dominance | |
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| Normal Random Variables | |
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| More on Second-Order Dominance | |
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| Exercises | |
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| Optimization Models | |
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| Introduction | |
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| A Deterministic Optimization Model | |
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| A General Solution Technique Based on Dynamic Programming | |
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| A Solution Technique for Concave Return Functions | |
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| The Knapsack Problem | |
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| Probabilistic Optimization Problems | |
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| A Gambling Model with Unknown Win Probabilities | |
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| An Investment Allocation Model | |
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| Exercises | |
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| Stochastic Dynamic Programming | |
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| The Stochastic Dynamic Programming Problem | |
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| Infinite Time Models | |
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| Optimal Stopping Problems | |
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| Exercises | |
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| Exotic Options | |
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| Introduction | |
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| Barrier Options | |
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| Asian and Lookback Options | |
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| Monte Carlo Simulation | |
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| Pricing Exotic Options by Simulation | |
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| More Efficient Simulation Estimators | |
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| Control and Antithetic Variables in the Simulation of Asian and Lookback Option Valuations | |
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| Combining Conditional Expectation and Importance Sampling in the Simulation of Barrier Option Valuations | |
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| Options with Nonlinear Payoffs | |
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| Pricing Approximations via Multiperiod Binomial Models | |
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| Continuous Time Approximations of Barrier and Lookback Options | |
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| Exercises | |
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| Beyond Geometric Brownian Motion Models | |
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| Introduction | |
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| Crude Oil Data | |
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| Models for the Crude Oil Data | |
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| Final Comments | |
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| Autoregressive Models and Mean Reversion | |
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| The Autoregressive Model | |
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| Valuing Options by Their Expected Return | |
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| Mean Reversion | |
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| Exercises | |
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| Index | |