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by Jichao Zhao, Robert M. Corless, Matt Davison
International workshop on symbolic-numerical computation Proceedings
http://publish.uwo.ca/~jzhao29/Last_SNC.pdf
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Abstract:
Abstract. We introduce the standard fourth order compact finite difference formulae. We show how these formulae apply in the special case of the heat equation. It is well known that the American option pricing problem may be formulated in terms of the Black Scholes partial differential equation (PDE) together with a free boundary condition. Standard methods allow this problem to be transformed into a moving boundary heat equation problem. We use the compact finite difference method to reduce this problem to a system of ordinary differential equations with specified initial conditions. We develop three ways of combining the resulting systems with methods designed to cope with free boundary values. We show that the compact finite difference scheme for the heat equation and for the American options pricing problem are unconditionally stable. After numerical comparison of these methods with a standard Crank Nicholson projected Successive Over Relaxation method, we conclude that the compact finite difference technique respresents an exciting new method for pricing American options. 1.
Citations
|
75
|
Compact finite difference schemes with spectral-like resolution
– LELE
- 1992
|
|
43
|
Efficient analytic approximation of American option values
– Barone-Adesi, Whaley
- 1987
|
|
17
|
The Stability of Numerical Boundary Treatments for Compact High-Order Finite-Difference Schemes
– Carpenter, Gottlieb, et al.
- 1993
|
|
13
|
The analytic valuation of the American options
– Kim
- 1990
|
|
4
|
An exploration of compact finite difference methods for the numerical Solution
– Ahmed
- 1997
|
|
4
|
FINDIF, a routine for generation of finite difference formulae, Share Library package 1994, and upgraded to n dimensions for “iguana
– Corless, Rokicki, et al.
|
|
3
|
A high order compact boundary value method for solving one dimensional heat equations
– Sun, Zhang
- 2002
|
|
3
|
Numerical methods and software for the pricing of American financial derivatives
– Pantazopoulos
- 1998
|
|
2
|
High order compact finite difference schemes for a nonlinear Black-Scholes equation
– Düring, Fournié, et al.
- 2003
|
|
2
|
Approximations for the values of American options
– Barone-Adesi, Elliott
- 1991
|
|
1
|
Convergence of a high-order compact finite difference schemes for a nonlinear Black-Scholes equation
– Düring, Fournié, et al.
|
|
1
|
The Saga of the American Put
– Barone-Adesi, Lugano
- 2003
|
|
1
|
J.Dewynne and S.Howison, Option Pricing: Mathematical Model and Computation
– Wilmott
- 1995
|
|
1
|
High-order compact difference schemes for computational mechanics[D
– Spotz
- 1995
|
|
1
|
X.Deng and W.Zheng, A new numerical method on American option pricing. Science in China, vol 45(3
– Gu, Shu
- 2002
|
