Although there are several publications on similar subjects, this book mainly focuses on pricing of options and bridges the gap between Mathematical Finance and Numerical Methodologies. The author collects the key contributions of several monographs and selected literature, values and displays their importance, and composes them here to create a work which has its own characteristics in content and style.This invaluable book provides working Matlab codes not only to implement the algorithms presented in the text, but also to help readers code their own pricing algorithms in their preferred programming languages. Availability of the codes under an Internet site is also offered by the author.Not only does this book serve as a textbook in related undergraduate or graduate courses, but it can also be used by those who wish to implement or learn pricing algorithms by themselves. The basic methods of option pricing are presented in a self-contained and unified manner, and will hopefully help readers improve their mathematical and computational backgrounds for more advanced topics.Errata(s)Errata
Fixed-Income Securities, Portfolio Management, and Mean-Variance Portfolio Optimization; Options and the No-Arbitrage Principle; Binomial Model, Valuation of European and American Options; Stochastic Integral and the Ito Lemma, Applications, Derivation and Solution of the Black-Scholes Equation and the Greeks; Pseudo-Random Numbers, Transformation of Random Variables, Generating Normal and Other Variates, Box-Muller and Marsaglia Methods; Option Pricing by Monte Carlo Simulations, Variance Reduction Techniques, and the Quasi-Monte Carlo Simulations; Finite Difference Methods for Solving Partial Differential Equations; Explicit, Implicit, and the Crank-Nicolson Methods for the Heat Equation and the Black-Scholes Equation, and the Relations to Tree Methods; Pricing European and American Options by Partial Differential Equations, and the Projected SOR Method.