Option Valuation

Hugo D. Junghenn is a professor of mathematics at the George Washington University. His research interests include functional analysis and semigroups.

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.