Helping readers accurately price a vast array of derivatives, this self-contained text explains how to solve complex functional equations through numerical methods. It addresses key computational methods in finance, including transform techniques, the finite difference method, and Monte Carlo simulation. Developed from his courses at Columbia University and the Courant Institute of New York University, the author also covers model calibration and optimization and describes techniques, such as Kalman and particle filters, for parameter estimation.
Table of Contents:
I Pricing and Valuation: Stochastic Processes and Risk-Neutral Pricing. Derivatives Pricing via Transform Techniques. Introduction to Finite Differences. Derivative Pricing via Numerical Solutions of PDEs. Derivative Pricing via Numerical Solutions of PIDEs. Simulation Methods for Derivatives Pricing. II Calibration and Estimation: Model Calibration. Filtering and Parameter Estimation. References. Index.
About the Author :
Ali Hirsa is head of Analytical Trading Strategy at Caspian Capital Management. Dr. Hirsa is also an adjunct professor at Columbia University and NYU's Courant Institute of Mathematical Sciences.
Review :
"The depth and breadth of this stand-alone textbook on computational methods in finance is astonishing. It brings together a full-spectrum of methods with many practical examples. … the purpose of the book is to aid the understanding and solving of current problems in computational finance. … an excellent synthesis of numerical methods needed for solving practical problems in finance. This book provides plenty of exercises and realistic case studies. Those who work through them will gain a deep understanding of the modern computational methods in finance. This uniquely comprehensive and well-written book will undoubtedly prove invaluable to many researchers and practitioners. In addition, it seems to be an excellent teaching book."
—Lasse Koskinen, International Statistical Review (2013), 81
"… there are several sections on topics that are rarely treated in textbooks: saddle point approximations, numerical solution of PIDEs, and others. There is also extensive material on model calibration, including interest rate models and filtering approaches. The book is a very comprehensive and useful reference for anyone, even with limited mathematical background, who wishes to quickly understand techniques from computational finance."
—Stefan Gerhold, Zentralblatt MATH 1260
"A natural polymath, the author is at once a teacher, a trader, a quant, and now an author of a book for the ages. The content reflects the author’s vast experience teaching master’s level courses at Columbia and NYU, while simultaneously researching and trading on quantitative finance in leading banks and hedge funds."
—Dr. Peter Carr, Global Head of Market Modeling, Morgan Stanley, and Executive Director of Masters in Math Finance, NYU Courant Institute of Mathematical Sciences
"A long-time expert in computational finance, Ali Hirsa brings his excellent expository skills to bear on not just one technique but the whole panoply, from finite difference solutions to PDEs/PIDEs through simulation to calibration and parameter estimation."
—Emanuel Derman, professor at Columbia University and author of Models Behaving Badly
