An Introduction to Financial Option Valuation

Mathematics, Stochastics and Computation

Desmond J. Higham

273 pages, parution le 01/10/2004

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Résumé

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.

L'auteur - Desmond J. Higham

Des Higham is a professor of mathematics at the University of Strathclyde. He was co-written two previous books, MATLAB Guide and Learning LaTeX.

Sommaire

Options
Option valuation preliminaries
Random variables
Computer simulation
Asset price movement
Asset price model: Part I
Asset price model: Part II
Black-Scholes PDE and formulas
More on hedging
The Greeks
More on the Black-Scholes formulas
Risk neutrality
Solving a nonlinear equation
Implied volatility
Monte Carlo method
Binomial method
Cash-or-nothing options
American options
Exotic options
Historical volatility
Monte Carlo Part II: variance reduction by antithetic variates
Monte Carlo Part III: variance reduction by control variates
Finite difference methods
Finite difference methods for the Black-Scholes PDE

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Desmond J. Higham
Parution	01/10/2004
Nb. de pages	273
Format	17 x 24,5
Couverture	Broché
Poids	655g
Intérieur	Noir et Blanc
EAN13	9780521547574
ISBN13	978-0-521-54757-4