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# Option Valuation

### Hardcover

Published: 23rd November 2011
Ships: 7 to 10 business days
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Option Valuation: A First Course in Financial Mathematics provides a straightforward introduction to the mathematics and models used in the valuation of financial derivatives. It examines the principles of option pricing in detail via standard binomial and stochastic calculus models. Developing the requisite mathematical background as needed, the text presents an introduction to probability theory and stochastic calculus suitable for undergraduate students in mathematics, economics, and finance.

The first nine chapters of the book describe option valuation techniques in discrete time, focusing on the binomial model. The author shows how the binomial model offers a practical method for pricing options using relatively elementary mathematical tools. The binomial model also enables a clear, concrete exposition of fundamental principles of finance, such as arbitrage and hedging, without the distraction of complex mathematical constructs. The remaining chapters illustrate the theory in continuous time, with an emphasis on the more mathematically sophisticated Black-Scholes-Merton model.

Largely self-contained, this classroom-tested text offers a sound introduction to applied probability through a mathematical finance perspective. Numerous examples and exercises help students gain expertise with financial calculus methods and increase their general mathematical sophistication. The exercises range from routine applications to spreadsheet projects to the pricing of a variety of complex financial instruments. Hints and solutions to odd-numbered problems are given in an appendix and a full solutions manual is available for qualifying instructors.

The text provides an introduction to classical material of mathematical finance, i.e. the notions of arbitrage, replication, and option pricing in the context of the discrete-time Cox-Ross-Rubinstein and the continuous-time Black-Scholes model, respectively. The book sticks out by not assuming any background in stochastics. All necessary concepts of probability theory, martingales, and It calculus are provided
Jan Kallsen, Zentralblatt MATH 1247

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.

ISBN: 9781439889114
ISBN-10: 1439889112
Series: Chapman & Hall/CRC Financial Mathematics Series
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 266
Published: 23rd November 2011
Dimensions (cm): 23.5 x 15.6  x 2.0
Weight (kg): 0.59