An Introduction to Financial Option Valuation

Mathematics, Stochastics and Computation
Erscheinungsjahr 2004
ISBN: 978-0-521-83884-9
Verlag: Cambridge University Press

Buch, Englisch, 296 Seiten, Format (B × H): 180 mm x 255 mm, Gewicht: 805 g

This is a lively textbook providing a solid introduction to financial option valuation for undergraduate students armed with a working knowledge of a first year calculus. Written in a series of short chapters, its self-contained treatment gives equal weight to applied mathematics, stochastics and computational algorithms. No prior background in probability, statistics or numerical analysis is required. Detailed derivations of both the basic asset price model and the Black–Scholes equation are provided along with a presentation of appropriate computational techniques including binomial, finite differences and in particular, variance reduction techniques for the Monte Carlo method. Each chapter comes complete with accompanying stand-alone MATLAB code listing to illustrate a key idea. Furthermore, the author has made heavy use of figures and examples, and has included computations based on real stock market data.

Autoren/Hrsg.

Higham, Desmond

Higham, Desmond J.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
• Wirtschaftswissenschaften Betriebswirtschaft Unternehmensfinanzen Finanzierung, Investition, Leasing
• Wirtschaftswissenschaften Finanzsektor & Finanzdienstleistungen Unternehmensfinanzierung

Inhaltsverzeichnis

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.

Über Autor(innen)

Higham, Desmond J.
Des Higham is a Professor of Mathematics at the University of Strathclyde. His previous books include MATLAB Guide (with Nicholas J. Higham, 2005) and Learning LaTeX (with David F. Griffiths, 1997).