About this product

Product Identifiers

PublisherCRC Press LLC

ISBN-101439829578

ISBN-139781439829578

eBay Product ID (ePID)78701678

Product Key Features

Number of Pages444 Pages

Publication NameComputational Methods in Finance

LanguageEnglish

SubjectInvestments & Securities / Derivatives, Probability & Statistics / General, Operations Research, General

Publication Year2012

TypeTextbook

AuthorAli Hirsa

Subject AreaMathematics, Business & Economics

SeriesChapman and Hall/Crc Financial Mathematics Ser.

FormatHardcover

Dimensions

Item Height1.1 in

Item Weight34.4 Oz

Item Length10.1 in

Item Width7.3 in

Additional Product Features

Intended AudienceCollege Audience

LCCN2012-017892

Reviews"... 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, "e 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." e"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 authore(tm)s vast experience teaching mastere(tm)s level courses at Columbia and NYU, while simultaneously researching and trading on quantitative finance in leading banks and hedge funds." e"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." e"Emanuel Derman, professor at Columbia University and author of Models Behaving Badly, "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. 'e¦ the purpose of the book is to aid the understanding and solving of current problems in computational finance. 'e¦ 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." 'e"Lasse Koskinen, International Statistical Review (2013), 81 "'e¦ 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." 'e"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'e(tm)s vast experience teaching master'e(tm)s level courses at Columbia and NYU, while simultaneously researching and trading on quantitative finance in leading banks and hedge funds." 'e"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." 'e"Emanuel Derman, professor at Columbia University and author of Models Behaving Badly, "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, 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, "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 MATH1260 "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, 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

Dewey Edition23/eng/20240124

IllustratedYes

Dewey Decimal332.64/5

Table Of ContentI Pricing and Valuation Stochastic Processes and Risk-Neutral Pricing Characteristic Function Stochastic Models of Asset Prices Valuing Derivatives under Various Measures Types of Derivatives Derivatives Pricing via Transform Techniques Derivatives Pricing via the Fast Fourier Transform Fractional Fast Fourier Transform Derivatives Pricing via the Fourier-Cosine (COS) Method Cosine Method for Path-Dependent Options Saddlepoint Method Introduction to Finite Differences Taylor Expansion Finite Difference Method Stability Analysis Derivative Approximation by Finite Differences: A Generic Approach Matrix Equations Solver Derivative Pricing via Numerical Solutions of PDEs Option Pricing under the Generalized Black-Scholes PDE Boundary Conditions and Critical Points Nonuniform Grid Points Dimension Reduction Pricing Path-Dependent Options in a Diffusion Framework Forward PDEs Finite Differences in Higher Dimensions Derivative Pricing via Numerical Solutions of PIDEs Numerical Solution of PIDEs (a Generic Example) American Options PIDE Solutions for Lévy Processes Forward PIDEs Calculation of g 1 and g 2 Simulation Methods for Derivatives Pricing Random Number Generation Samples from Various Distributions Models of Dependence Brownian Bridge Monte Carlo Integration Numerical Integration of Stochastic Differential Equations Simulating SDEs under Different Models Output/Simulation Analysis Variance Reduction Techniques II Calibration and Estimation Model Calibration Calibration Formulation Calibration of a Single Underlier Model Interest Rate Models Model Risk Optimization and Optimization Methodology Construction of the Discount Curve Arbitrage Restrictions on Option Premiums Interest Rate Definitions Filtering and Parameter Estimation Filtering The Likelihood Function Kalman Filter Non-Linear Filters Extended Kalman Filter Unscented Kalman Filter Square Root Unscented Kalman Filter (SR UKF) Particle Filter Markov Chain Monte Carlo (MCMC) References Index Problems appear at the end of each chapter.

SynopsisAs 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.

LC Classification NumberHG6024.A3