The Evaluation of American Option Prices Under Stochastic Volatility and Jump-Diffusion Dynamics Using the Method of Lines

University of Technology Sydney Research Paper No. 219

43 Pages Posted: 12 May 2008

See all articles by Carl Chiarella

Carl Chiarella

University of Technology, Sydney - UTS Business School, Finance Discipline Group

Boda Kang

AMP

Gunter H. Meyer

Georgia Institute of Technology - Mathematics

Andrew Ziogas

University of Technology Sydney (UTS) - School of Finance and Economics

Multiple version iconThere are 2 versions of this paper

Date Written: April 1, 2008

Abstract

This paper considers the problem of numerically evaluating American option prices when the dynamics of the underlying are driven by both stochastic volatility following the square root process of Heston (1993), and by a Poisson jump process of the type originally introduced by Merton (1976). We develop a method of lines algorithm to evaluate the price as well as the delta and gamma of the option, thereby extending the method developed by Meyer (1998) for the case of jump-diffusion dynamics. The accuracy of the method is tested against two numerical methods that directly solve the integro-partial differential pricing equation. The first is an extension to the jump-diffusion situation of the componentwise splitting method of Ikonen & Toivanen (2007). The second method is a Crank-Nicolson scheme that is solved using projected successive over relaxation which is taken as the benchmark. The relative efficiency of these methods for computing the American call option price, delta, gamma and free boundary is analysed. If one seeks an algorithm that gives not only the price but also the delta and gamma to the same level of accuracy for a given computational effort then the method of lines seems to perform best amongst the methods considered.

Keywords: American options, stochastic volatility, jump-diffusion processes, Volterra integral equations, free boundary problem, method of lines

JEL Classification: C61, D11

Suggested Citation

Chiarella, Carl and Kang, Boda and Meyer, Gunter H. and Ziogas, Andrew, The Evaluation of American Option Prices Under Stochastic Volatility and Jump-Diffusion Dynamics Using the Method of Lines (April 1, 2008). University of Technology Sydney Research Paper No. 219, Available at SSRN: https://ssrn.com/abstract=1129062 or http://dx.doi.org/10.2139/ssrn.1129062

Carl Chiarella (Contact Author)

University of Technology, Sydney - UTS Business School, Finance Discipline Group ( email )

PO Box 123
Broadway, NSW 2007
Australia
+61 2 9514 7719 (Phone)
+61 2 9514 7711 (Fax)

HOME PAGE: http://www.business.uts.edu.au/finance/

Boda Kang

AMP ( email )

Sydney, NSW
Australia
0430976988 (Phone)
2154 (Fax)

Gunter H. Meyer

Georgia Institute of Technology - Mathematics ( email )

United States

Andrew Ziogas

University of Technology Sydney (UTS) - School of Finance and Economics ( email )

Haymarket
Sydney, NSW 2007
Australia

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