Computational Methods in Finance
As today’s financial products have become more complex, quantitative analysts, financial engineers, and others in the financial industry now require robust techniques for numerical analysis. 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.
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The book covers many interesting and challenging topics like Fourier transformation methods, finite difference methods, Kalman filtering and Monte-Carlo simulation etc. If one understands theories presented in the book and puts these theories into practice by writing computer programs to solve problems at the end of each chapter, one is well prepared for a career in quantitative finance.
The book is well-written and easy to follow. The author usually breaks down a complex problem into steps with clear mathematical derivations. For example, using tri-diagonal method to solve Partial Integro-Differential Equation (PIDE) of an American option is mathematically complex. The author analyzes and breaks down the problem into sections with clear derivations for each section. As a result, most people with decent math background can understand these derivations and can write a computer program solving PIDE to get price of an American option.