Interest and Present Value Compound Interest Annuities Bonds Rate of Return Probability Spaces Sample Spaces and Events Discrete Probability Spaces General Probability Spaces Conditional Probability Independence Random Variables Definition and General Properties Discrete Random Variables Continuous Random Variables Joint Distributions Independent Random Variables Sums of Independent Random Variables Options and Arbitrage Arbitrage Classification of Derivatives Forwards Currency Forwards Futures Options Properties of Options Dividend-Paying Stocks Discrete-Time Portfolio Processes Discrete-Time Stochastic Processes Self-Financing Portfolios Option Valuation by Portfolios Expectation of a Random Variable Discrete Case: Definition and Examples Continuous Case: Definition and Examples Properties of Expectation Variance of a Random Variable The Central Limit Theorem The Binomial Model Construction of the Binomial Model Pricing a Claim in the Binomial Model The Cox-Ross-Rubinstein Formula Conditional Expectation and Discrete-Time Martingales Definition of Conditional Expectation Examples of Conditional Expectation Properties of Conditional Expectation Discrete-Time Martingales The Binomial Model Revisited Martingales in the Binomial Model Change of Probability American Claims in the Binomial Model Stopping Times Optimal Exercise of an American Claim Dividends in the Binomial Model The General Finite Market Model Stochastic Calculus Differential Equations Continuous-Time Stochastic Processes Brownian Motion Variation of Brownian Paths Riemann-Stieltjes Integrals Stochastic Integrals The Ito-Doeblin Formula Stochastic Differential Equations The Black-Scholes-Merton Model The Stock Price SDE Continuous-Time Portfolios The Black-Scholes-Merton PDE Properties of the BSM Call Function Continuous-Time Martingales Conditional Expectation Martingales: Definition and Examples Martingale Representation Theorem Moment Generating Functions Change of Probability and Girsanov''s Theorem The BSM Model Revisited Risk-Neutral Valuation of a Derivative Proofs of the Valuation Formulas Valuation under P The Feynman-Kac Representation Theorem Other Options Currency Options Forward Start Options Chooser Options Compound Options Path-Dependent Derivatives Quantos Options on Dividend-Paying Stocks American Claims in the BSM Model Appendix A: Sets and Counting Appendix B: Solution of the BSM PDE Appendix C: Analytical Properties of the BSM Call Function Appendix D: Hints and Solutions to Odd-Numbered Problems Bibliography Index Exercises appear at the end of each chapter. Dividend-Paying Stocks Discrete-Time Portfolio Processes Discrete-Time Stochastic Processes Self-Financing Portfolios Option Valuation by Portfolios Expectation of a Random Variable Discrete Case: Definition and Examples Continuous Case: Definition and Examples Properties of Expectation Variance of a Random Variable The Central Limit Theorem The Binomial Model Construction of the Binomial Model Pricing a Claim in the Binomial Model The Cox-Ross-Rubinstein Formula Conditional Expectation and Discrete-Time Martingales Definition of Conditional Expectation Examples of Conditional Expectation Properties of Conditional Expectation Discrete-Time Martingales The Binomial Model Revisited Martingales in the Binomial Model Change of Probability American Claims in the Binomial Model Stopping Times Optimal Exercise of an American Claim Dividends in the Binomial Model The General Finite Market Model Stochastic Calculus Differential Equations Continuous-Time Stochastic Processes Brownian Motion Variation of Brownian Paths Riemann-Stieltjes Integrals Stochastic Integrals The Ito-Doeblin Formula Stochastic Differential Equations The Black-Scholes-Merton Model The Stock Price SDE Continuous-Time Portfolios The Black-Scholes-Merton PDE Properties of the BSM Call Function Continuous-Time Martingales Conditional Expectation Martingales: Definition and Examples Martingale Representation Theorem Moment Generating Functions Change of Probability and Girsanov''s Theorem The BSM Model Revisited Risk-Neutral Valuation of a Derivative Proofs of the Valuation Formulas Valuation under P The Feynman-Kac Representation Theorem Other Options Currency Options Forward Start Options Chooser Options Compound Options Path-Dependent Derivatives Quantos Options on Dividend-Paying Stocks American Claims in the BSM Model Appendix A: Sets and Counting Appendix B: Solution of the BSM PDE Appendix C: Analytical Properties of the BSM Call Function Appendix D: Hints and Solutions to Odd-Numbered Problems Bibliography Index Exercises appear at the end of each chapter. ectation Properties of Conditional Expectation Discrete-Time Martingales The Binomial Model Revisited Martingales in the Binomial Model Change of Probability American Claims in the Binomial Model Stopping Times Optimal Exercise of an American Claim Dividends in the Binomial Model The General Finite Market Model Stochastic Calculus Differential Equations Continuous-Time Stochastic Processes Brownian Motion Variation of Brownian Paths Riemann-Stieltjes Integrals Stochastic Integrals The Ito-Doeblin Formula Stochastic Differential Equations The Black-Scholes-Merton Model The Stock Price SDE Continuous-Time Portfolios The Black-Scholes-Merton PDE Properties of the BSM Call Function Continuous-Time Martingales Conditional Expectation Martingales: Definition and Examples Martingale Representation Theorem Moment Generating Functions Change of Probability and Girsanov''s Theorem The BSM Model Revisited Risk-Neutral Valuation of a Derivative Proofs of the Valuation Formulas Valuation under P The Feynman-Kac Representation Theorem Other Options Currency Options Forward Start Options Chooser Options Compound Options Path-Dependent Derivatives Quantos Options on Dividend-Paying Stocks American Claims in the BSM Model Appendix A: Sets and Counting Appendix B: Solution of the BSM PDE Appendix C: Analytical Properties of the BSM Call Function Appendix D: Hints and Solutions to Odd-Numbered Problems Bibliography Index Exercises appear at the end of each chapter. uous-Time Portfolios The Black-Scholes-Merton PDE Properties of the BSM Call Function Continuous-Time Martingales Conditional Expectation Martingales: Definition and Examples Martingale Representation Theorem Moment Generating Functions Change of Probability and Girsanov''s Theorem The BSM Model Revisited Risk-Neutral Valuation of a Derivative Proofs of the Valuation Formulas Valuation under P The Feynman-Kac Representation Theorem Other Options Currency Options Forward Start Options Chooser Options Compound Options Path-Dependent Derivatives Quantos Options on Dividend-Paying Stocks American Claims in the BSM Model Appendix A: Sets and Counting Appendix B: Solution of the BSM PDE Appendix C: Analytical Properties of the BSM Call Function Appendix D: Hints and Solutions to Odd-Numbered Problems Bibliography Index Exercises appear at the end of each chapter. aims in the BSM Model Appendix A: Sets and Counting Appendix B: Solution of the BSM PDE Appendix C: Analytical Properties of the BSM Call Function Appendix D: Hints and Solutions to Odd-Numbered Problems Bibliography Index Exercises appear at the end of each chapter.