An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation / Edition 1

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Overview

This book is intended for use in a rigorous introductory PhD level course in econometrics, or in a field course in econometric theory. It covers the measure-theoretical foundation of probability theory, the multivariate normal distribution with its application to classical linear regression analysis, various laws of large numbers, central limit theorems and related results for independent random variables as well as for stationary time series, with applications to asymptotic inference of M-estimators, and maximum likelihood theory. Some chapters have their own appendices containing the more advanced topics and/or difficult proofs. Moreover, there are three appendices with material that is supposed to be known. Appendix I contains a comprehensive review of linear algebra, including all the proofs. Appendix II reviews a variety of mathematical topics and concepts that are used throughout the main text, and Appendix III reviews complex analysis. Therefore, this book is uniquely self-contained.

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Editorial Reviews

From the Publisher
"...well organized and well written...an excellent introductory text. It will be useful to students from a wide range of backgrounds and an essential complement to the standard undergraduate course which embeds mathematical finance into probability theory." UK Nonlinear News
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Product Details

  • ISBN-13: 9780521547574
  • Publisher: Cambridge University Press
  • Publication date: 3/31/2004
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 296
  • Product dimensions: 6.85 (w) x 9.72 (h) x 0.71 (d)

Meet the Author

Des Higham is a Professor of Mathematics at the University of Strathclyde. He has written 2 previous books, MATLAB Guide 0898715164 and Learning LaTeX 08988715164.

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Table of Contents

1. Introduction; 2. Option valuation preliminaries; 3. Random variables; 4. Computer simulation; 5. Asset price movement; 6. Asset price model: part I; 7. Asset price model: part II; 8. Black-Scholes PDE and formulas; 9. More on hedging; 10. The Greeks; 11. More on the Black-Scholes formulas; 12. Risk neutrality; 13. Solving a nonlinear equation; 14. Implied volatility; 15. The Monte Carlo method; 16. The binomial method; 17. Cash-or-nothing options; 18. American options; 19. Exotic options; 20. Historical volatility; 21. Monte Carlo part II: variance reduction by antithetic variates; 22. Monte Carlo part III: variance reduction by control variates; 23. Finite difference methods; 24. Finite difference methods for the Black-Scholes PDE.

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