An introduction to financial mathematics : option valuation

Content: Cover
 Half Title
 Title Page
 Copyright Page
 Dedication
 Table of Contents
 Preface
 1: Basic Finance
 1.1 Interest
 *1.2 Inflation
 1.3 Annuities
 1.4 Bonds
 *1.5 Internal Rate of Return
 1.6 Exercises
 2: Probability Spaces
 2.1 Sample Spaces and Events
 2.2 Discrete Probability Spaces
 2.3 General Probability Spaces
 2.4 Conditional Probability
 2.5 Independence
 2.6 Exercises
 3: Random Variables
 3.1 Introduction
 3.2 General Properties of Random Variables
 3.3 Discrete Random Variables
 3.4 Continuous Random Variables
 3.5 Joint Distributions of Random Variables 3.6 Independent Random Variables3.7 Identically Distributed Random Variables
 3.8 Sums of Independent Random Variables
 3.9 Exercises
 4: Options and Arbitrage
 4.1 The Price Process of an Asset
 4.2 Arbitrage
 4.3 Classification of Derivatives
 4.4 Forwards
 4.5 Currency Forwards
 4.6 Futures
 *4.7 Equality of Forward and Future Prices
 4.8 Call and Put Options
 4.9 Properties of Options
 4.10 Dividend-Paying Stocks
 4.11 Exotic Options
 *4.12 Portfolios and Payoff Diagrams
 4.13 Exercises
 5: Discrete-Time Portfolio Processes
 5.1 Discrete Time Stochastic Processes 5.2 Portfolio Processes and the Value Process5.3 Self-Financing Trading Strategies
 5.4 Equivalent Characterizations of Self-Financing
 5.5 Option Valuation by Portfolios
 5.6 Exercises
 6: Expectation
 6.1 Expectation of a Discrete Random Variable
 6.2 Expectation of a Continuous Random Variable
 6.3 Basic Properties of Expectation
 6.4 Variance of a Random Variable
 6.5 Moment Generating Functions
 6.6 The Strong Law of Large Numbers
 6.7 The Central Limit Theorem
 6.8 Exercises
 7: The Binomial Model
 7.1 Construction of the Binomial Model 7.2 Completeness and Arbitrage in the Binomial Model7.3 Path-Independent Claims
 *7.4 Path-Dependent Claims
 7.5 Exercises
 8: Conditional Expectation
 8.1 Definition of Conditional Expectation
 8.2 Examples of Conditional Expectations
 8.3 Properties of Conditional Expectation
 8.4 Special Cases
 *8.5 Existence of Conditional Expectation
 8.6 Exercises
 9: Martingales in Discrete Time Markets
 9.1 Discrete Time Martingales
 9.2 The Value Process as a Martingale
 9.3 A Martingale View of the Binomial Model
 9.4 The Fundamental Theorems of Asset Pricing
 *9.5 Change of Probability 9.6 Exercises10: American Claims in Discrete-Time Markets
 10.1 Hedging an American Claim
 10.2 Stopping Times
 10.3 Submartingales and Supermartingales
 10.4 Optimal Exercise of an American Claim
 10.5 Hedging in the Binomial Model
 10.6 Optimal Exercise in the Binomial Model
 10.7 Exercises
 11: Stochastic Calculus
 11.1 Continuous-Time Stochastic Processes
 11.2 Brownian Motion
 11.3 Stochastic Integrals
 11.4 The Ito-Doeblin Formula
 11.5 Stochastic Differential Equations
 11.6 Exercises
 12: The Black-Scholes-Merton Model
 12.1 The Stock Price SDE
 12.2 Continuous-Time Portfolios