TUM Library

Earlier edition: Introduction to financial mathematics / Kevin J. Hastings.

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

Introduction to Financial Mathematics: Option Valuation, Second Edition is a well-rounded primer to the mathematics and models used in the valuation of financial derivatives. The book consists of fteen chapters, the rst ten of which develop option valuation techniques in discrete time, the last ve describing the theory in continuous time. The first half of the textbook develops basic finance and probability. The author then treats the binomial model as the primary example of discrete-time option valuation. The final part of the textbook examines the Black-Scholes model. The book is written to provide a straightforward account of the principles of option pricing and examines these principles in detail using standard discrete and stochastic calculus models. Additionally, the second edition has new exercises and examples, and includes many tables and graphs generated by over 30 MS Excel VBA modules available on the author's webpage https://home.gwu.edu/~hdj/.

OCLC-licensed vendor bibliographic record.