Numerical schemes for pricing Asian options under state-dependent regime-switching jump-diffusion models

Dang, Duy-Minh, Nguyen, Duy and Sewell, Granville (2016) Numerical schemes for pricing Asian options under state-dependent regime-switching jump-diffusion models. Computers and Mathematics with Applications, 71 1: 443-458. doi:10.1016/j.camwa.2015.12.017


Author Dang, Duy-Minh
Nguyen, Duy
Sewell, Granville
Title Numerical schemes for pricing Asian options under state-dependent regime-switching jump-diffusion models
Journal name Computers and Mathematics with Applications   Check publisher's open access policy
ISSN 1873-7668
0898-1221
Publication date 2016-01-01
Year available 2015
Sub-type Article (original research)
DOI 10.1016/j.camwa.2015.12.017
Open Access Status Not Open Access
Volume 71
Issue 1
Start page 443
End page 458
Total pages 16
Place of publication Kidlington, Oxford, United Kingdom
Publisher Pergamon Press
Language eng
Formatted abstract
We study the pricing problem of Asian options when the underlying asset price follows a very general state-dependent regime-switching jump–diffusion process via a partial differential equation approach. 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). We prove existence of the solution to this system of PIDEs by the method of upper and lower solutions via constructing a monotonic sequence of approximating solutions whose limit is a strong solution of the PIDE system. We then propose several numerical schemes for solving the system of PIDEs. One of the proposed schemes is built upon the constructive proof, hence its results are provably convergent to the solution of the system of PIDEs. We illustrate the accuracy of the proposed methods by several numerical examples.
Keyword Asian options
Regime-switching
Jump–diffusion
System of partial integro-differential equations
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ
Additional Notes Published online 29 December 2015

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2016 Collection
 
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Created: Mon, 14 Dec 2015, 23:22:24 EST by Duy-minh Dang on behalf of Mathematics