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Computational Methods in Finance
Covering advanced quantitative techniques, Computational Methods in Finance explains how to solve complex functional equations through numerical methods.
The first part of the book describes pricing methods for numerous derivatives under a variety of models. The book reviews common processes for modeling assets in different markets. It then examines many computational approaches for pricing derivatives. These include transform techniques, such as the fast Fourier transform, the fractional fast Fourier transform, the Fourier-cosine method, and saddlepoint method; the finite difference method for solving PDEs in the diffusion framework and PIDEs in the pure jump framework; and Monte Carlo simulation.
The next part focuses on essential steps in real-world derivative pricing. The author discusses how to calibrate model parameters so that model prices are compatible with market prices. He also covers various filtering techniques and their implementations and gives examples of filtering and parameter estimation.
Developed from the author’s courses at Columbia University and the Courant Institute of New York University, this self-contained text is designed for graduate students in financial engineering and mathematical finance as well as practitioners in the financial industry. It will help readers accurately price a vast array of derivatives.
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
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.
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ISBN 9781439829578, September 2012, 444 pp