Pricing Financial Instruments: The Finite Difference Method / Edition 1

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Pricing Financial Instruments Numerical methods for the solution of financial instrument pricing equations are fast becoming essential for practitioners of modern quantitative finance. Among the most promising of these new computational finance techniques is the finite difference method-yet, to date, no single resource has presented a quality, comprehensive overview of this revolutionary quantitative approach to risk management. Pricing Financial Instruments, researched and written by Domingo Tavella and Curt Randall, two of the chief proponents of the finite difference method, presents a logical framework for applying the method of finite difference to the pricing of financial derivatives. Detailing the algorithmic and numerical procedures that are the foundation of both modern mathematical finance and the creation of financial products-while purposely keeping mathematical complexity to a minimum-this long-awaited book demonstrates how the techniques described can be used to accurately price simple and complex derivative structures. From a summary of stochastic pricing processes and arbitrage pricing arguments, through the analysis of numerical schemes and the implications of discretization-and ending with case studies that are simple yet detailed enough to demonstrate the capabilities of the methodology-Pricing Financial Instruments explores areas that include:

• Pricing equations and the relationship between European and American derivatives

• Detailed analyses of different stability analysis approaches

• Continuous and discrete sampling models for path dependent options

• One-dimensional and multi-dimensional coordinate transformations

• Numerical examples of barrier options, Asian options, forward swaps, and more
With an emphasis on how numerical solutions work and how the approximations involved affect the accuracy of the solutions, Pricing Financial Instruments takes us through doors opened wide by Black, Scholes, and Merton-and the arbitrage pricing principles they introduced in the early 1970s-to provide a step-by-step outline for sensibly interpreting the output of standard numerical schemes. It covers the understanding and application of today's finite difference method, and takes the reader to the next level of pricing financial instruments and managing financial risk.

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Editorial Reviews

This book presents a framework for applying the method of finite differences to the pricing of financial derivatives. It is structured with an emphasis on understanding how numerical schemes work, and how the approximations involved affect the accuracy of the solution. Coverage includes stochastic processes and arbitrage pricing arguments, the derivation of pricing equations, analysis of numerical schemes, and coordinate transformation. Case studies demonstrate the capabilities of the methodology presented. Material is aimed primarily at practitioners, but the book can be used as a reference text in financial engineering coursework. Although mathematical complexity has been reduced to a minimum, some background in derivative pricing and linear algebra is required. Tavella is a risk management and financial systems design consultant; Randall is involved with software synthesis technology for the finance industry. Annotation c. Book News, Inc., Portland, OR (
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Product Details

Meet the Author

DOMINGO TAVELLA, Ph.D., is President of Octanti Associates, a consulting firm in risk management and financial systems design. He is the founder and chief editor of the Journal of Computational Finance, and has pioneered the application of advanced numerical techniques in pricing and risk analysis in the financial and insurance industries. Before founding Octanti Associates, Dr. Tavella was director of financial engineering at Integral Development Corporation and vice president at Bankers Trust Securities. Prior to that, he was a scientist at Stanford University and NASA Ames Research Center.

CURT RANDALL, Ph.D.,is a Principal and Vice President of Applications at SciComp Inc., a leading developer of software synthesis technology for the finance industry. He has extensive experience in the application of finite difference methods to a variety of disciplines. Prior to joining SciComp, Dr. Randall developed computational methods for advanced simulations at Schlumberger Corporation. Before that, he was a research scientist at Lawrence Livermore National Laboratory.

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Table of Contents

The Pricing Equations.

Analysis of Finite Difference Methods.

Special Issues.

Coordinate Transformations.

Numerical Examples.


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