Computational Methods in Finance

Ali Hirsa is a Professor and director of the Center for Artificial Intelligence in Business Analytics and Financial Technology and director of the Financial Engineering Program in the Industrial Engineering & Operations Research Department at Columbia University in the City of New York. He is also Chief Scientific Officer at ASK2.ai and Managing Partner at Sauma Capital, LLC, a New York Hedge Fund. Previously he was a Partner and Head of Analytical Trading Strategy at Caspian Capital Management, LLC. Ali has worked in a variety of quantitative positions at Morgan Stanley, DV Trading, Banc of America Securities, and Prudential Securities. Ali was also a Fellow at Courant Institute of New York University in the Mathematics of Finance Program from 2004 to 2014. Ali is the author of “Computational Methods in Finance,” Chapman & Hall/CRC 2012, co-author of “An Introduction to Mathematics of Financial Derivatives,” third edition, Academic Press with Salih Neftci, and the editor-in-chief of the Journal of Investment Strategies. He is a frequent speaker at academic and practitioner conferences. Ali received his Ph.D. in Applied Mathematics from the University of Maryland at College Park under the supervision of Professors Howard C. Elman and Dilip B. Madan.

• 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. Credit Derivatives and Loan Models. Simulation Methods for Derivatives Pricing. Model Calibration. Filtering and Parameter Estimation.

Praise for the Previous Edition"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