An Iterative Method for Pricing American Options Under Jump-Diffusion Models

17 Pages Posted: 27 Jan 2011

See all articles by Santtu Salmi

Santtu Salmi

University of Jyväskylä - Department of Mathematical Information Technology

Jari Toivanen

University of Jyväskylä - Department of Mathematical Information Technology; Stanford University

Date Written: January 26, 2011

Abstract

We propose an iterative method for pricing American options under jump-diffusion models. A finite difference discretization is performed on the partial integro-differential equation, and the American option pricing problem is formulated as a linear complementarity problem (LCP). Jump-diffusion models include an integral term, which causes the resulting system to be dense. We propose an iteration to solve the LCPs efficiently and prove its convergence. Numerical examples with Kou's and Merton's jump-diffusion models show that the resulting iteration converges rapidly.

Keywords: American Option, Jump-Diffusion Model, Finite Difference Method, Linear Complementarity Problem, Iterative Method

JEL Classification: C63, G13

Suggested Citation

Salmi, Santtu and Toivanen, Jari, An Iterative Method for Pricing American Options Under Jump-Diffusion Models (January 26, 2011). Available at SSRN: https://ssrn.com/abstract=1748943 or http://dx.doi.org/10.2139/ssrn.1748943

Santtu Salmi (Contact Author)

University of Jyväskylä - Department of Mathematical Information Technology ( email )

P.O. Box 35 (Agora)
Jyvaskyla, 40014
Finland

Jari Toivanen

University of Jyväskylä - Department of Mathematical Information Technology ( email )

P.O. Box 35 (Agora)
Jyvaskyla, 40014
Finland

Stanford University ( email )

Stanford, CA 94305
United States

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