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The numerical solution of the American option pricing problem : finite difference and transform approaches /

The early exercise opportunity of an American option makes it challenging to price and an array of approaches have been proposed in the vast literature on this topic. In The Numerical Solution of the American Option Pricing Problem, Carl Chiarella, Boda Kang and Gunter Meyer focus on two numerical a...

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Bibliographic Details
Main Authors: Chiarella, Carl (Author)
Corporate Authors: World Scientific (Firm)
Group Author: Kang, Boda; Meyer, Gunter H.
Published: World Scientific Pub. Co.,
Publisher Address: Singapore ; Hackensack, N.J. :
Publication Dates: 2015.
Literature type: eBook
Language: English
Subjects:
Options (Finance) > United States.
Options (Finance) > Mathematical models.
Electronic books.
Online Access: http://www.worldscientific.com/worldscibooks/10.1142/8736#t=toc
Summary: The early exercise opportunity of an American option makes it challenging to price and an array of approaches have been proposed in the vast literature on this topic. In The Numerical Solution of the American Option Pricing Problem, Carl Chiarella, Boda Kang and Gunter Meyer focus on two numerical approaches that have proved useful for finding all prices, hedge ratios and early exercise boundaries of an American option. One is a finite difference approach which is based on the numerical solution of the partial differential equations with the free boundary problem arising in American option pricing, including the method of lines, the component wise splitting and the finite difference with PSOR. The other approach is the integral transform approach which includes Fourier or Fourier Cosine transforms. Written in a concise and systematic manner, Chiarella, Kang and Meyer explain and demonstrate the advantages and limitations of each of them based on their and their co-workers' experiences with these approaches over the years.
Carrier Form: 1 online resource (ix,212pages) : illustrations (some color), color ports
Bibliography: Includes bibliographical references (pages 201-206) and index.
ISBN: 9789814452625
Index Number: HG6024
CLC: F830.9
Contents: 1. Introduction -- 2. The Merton and Heston model for a call. 2.1. The model -- 3. American call options under jump-diffusion processes. 3.1. Introduction. 3.2. The problem statement - Merton's model. 3.3. Jamshidian's representation. 3.4. Limit of the early exercise boundary at expiry. 3.5. The American call with log-normal jumps. 3.6. Properties of the free boundary at expiry. 3.7. Numerical implementation. 3.8. Numerical results -- 4. American option prices under stochastic volatility and jump-diffusion dynamics - The transform approach. 4.1. Introduction. 4.2. The problem statement - The Merton-Heston model. 4.3. The integral transform solution. 4.4. The Martingale representation. 4.5. Conclusion -- 5. Representation and numerical approximation of American option prices under Heston. 5.1. Introduction. 5.2. Problem statement - The Heston model. 5.3. Finding the density function using integral transforms. 5.4. Solution for the American call option. 5.5. Numerical scheme for the free surface. 5.6. Conclusion -- 6. Fourier cosine expansion approach. 6.1. Heston model. 6.2. The pricing method for European options. 6.3. The pricing method for American options. 6.4. Two (higher) dimensional COS methods. 6.5. Numerical results -- 7. A numerical approach to pricing American call options under SVJD. 7.1. The PDE formulation. 7.2. Numerical solution using finite differences with projected overrelaxation (PSOR). 7.3. Componentwise splitting for the SVJD call. 7.4. The method of lines for the SVJD call. 7.5. Numerical results -- 8. Conclusion.

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