## An Introduction to Computational FinanceAlthough 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 |

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### Contents

Introduction | 1 |

Option Pricing and Binomial Methods | 35 |

Stochastic Diﬀerential Equations | 71 |

The BlackScholes Equation | 111 |

Random Numbers and Monte Carlo Simulation | 139 |

Option Pricing by Partial Diﬀerential Equations | 195 |

Appendix A A Short Introduction to Matlab | 263 |

289 | |

295 | |

### Common terms and phrases

Algorithm American options approximation arbitrage asset prices assumed beta binomial lattice binomial method binomial model Black-Scholes equation Black-Scholes PDE bond boundary conditions built-in function calculated call and put call option cash ﬂow closed-form solution coeﬃcient computed considered convergence convexity corresponding Crank-Nicolson method deﬁned deﬁnition derivatives discrete dividends eﬃcient Euler-Maruyama method European call European options example exercise explicit method ﬁle ﬁnance ﬁnancial ﬁnd ﬁnite diﬀerence methods ﬁrst geometric Brownian motion given grid Halton sequences heat equation Hence implementation Itˆo integral iterative lemma linear Matlab Matlab script matrix maturity modiﬁed Monte Carlo method Monte Carlo simulation no-arbitrage principle obtained option price parameters paths payoﬀ portfolio problem put option quadratic random numbers random variable risk-free interest rate risk-neutral samples shown in Fig sigma Smax Smin solving stochastic processes strike price theorem transformation underlying asset variance vector volatility Wiener process yield zero