Numerical Schemes for Pricing Asian Options Under State-Dependent Regime-Switching Jump-Diffusion Models

30 Pages Posted: 1 Mar 2015 Last revised: 26 Feb 2018

See all articles by Duy-Minh Dang

Duy-Minh Dang

University of Queensland - School of Mathematics and Physics

Duy Nguyen

Marist College - Department of Mathematics

Granville Sewell

University of Texas at El Paso

Date Written: October 28, 2015

Abstract

We propose numerical schemes for pricing Asian options when the underlying asset price follows a very general state-dependent regime-switching jump-diffusion process. Under this model, the price of the option can be obtained by solving a highly complex system of coupled two-dimensional parabolic partial integro-differential equations (PIDEs) via iterative techniques. One of the proposed schemes is provably convergent to the solution of the system of PIDEs. In addition, by treating the coupling and integral terms explicitly, over each iteration of the scheme, the pricing problem under this scheme can be partitioned into independent pricing sub-problem, with communication at the end of the iteration. Hence, this method allows for a very natural and easy-to-implement, yet efficient, parallelization of the solution process on multi-core architectures. We illustrate the accuracy and efficiency of the proposed methods by several numerical examples.

Keywords: Asian options, regime-switching, jump-diffusion, system of partial integro-differential equations, parallel computing

Suggested Citation

Dang, Duy-Minh and Nguyen, Duy and Sewell, Granville, Numerical Schemes for Pricing Asian Options Under State-Dependent Regime-Switching Jump-Diffusion Models (October 28, 2015). Available at SSRN: https://ssrn.com/abstract=2571507 or http://dx.doi.org/10.2139/ssrn.2571507

Duy-Minh Dang (Contact Author)

University of Queensland - School of Mathematics and Physics ( email )

Priestly Building
St Lucia
Brisbane, Queesland 4067
Australia

HOME PAGE: http://people.smp.uq.edu.au/Duy-MinhDang/

Duy Nguyen

Marist College - Department of Mathematics ( email )

NY
United States

HOME PAGE: http://sites.google.com/site/nducduy/

Granville Sewell

University of Texas at El Paso ( email )

500 W University Ave
El Paso, TX 79902
United States

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