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A Discontinuous Galerkin Method for Pricing American Options Under the Constant Elasticity of Variance Model

Published online by Cambridge University Press:  24 March 2015

David P. Nicholls  and
Andrew Sward
David P. Nicholls*
Affiliation:
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL 60607, USA
Andrew Sward
Affiliation:
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL 60607, USA
*
*Corresponding author. Email addresses: [email protected] (D. P. Nicholls), [email protected] (A. Sward)
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Abstract

The pricing of option contracts is one of the classical problems in Mathematical Finance. While useful exact solution formulas exist for simple contracts, typically numerical simulations are mandated due to the fact that standard features, such as early-exercise, preclude the existence of such solutions. In this paper we consider derivatives which generalize the classical Black-Scholes setting by not only admitting the early-exercise feature, but also considering assets which evolve by the Constant Elasticity of Variance (CEV) process (which includes the Geometric Brownian Motion of Black-Scholes as a special case). In this paper we investigate a Discontinuous Galerkin method for valuing European and American options on assets evolving under the CEV process which has a number of advantages over existing approaches including adaptability, accuracy, and ease of parallelization.

Keywords

91G2091G6065M70Option pricingPDE methodsCEV processDiscontinuous Galerkin method
Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 3 , March 2015 , pp. 761 - 778
Copyright
Copyright © Global-Science Press 2015 

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