CiNii Books - 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 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.

Table of Contents

The PDE Approach: Method of Lines
Finite Difference Schemes
Sparse Grid Method
The Integral Transform Approach: Fourier Transform
Laplace Transform
Mellin Transform
The Fourier Cosine Expansion Approach: FFT
Fourier Cosine Expansion
Fourier Space Time Stepping
Examples: Spread Options
Compound Options
Max and Min Options
Barrier Options
Conclusions.

by "Nielsen BookData"

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

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