Year: 2020
Author: Zhiqiang Zhou, Jingtang Ma, Zhijun Tan, Han Wang, Zhiqiang Zhou, Zhijun Tan
Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 2 : pp. 497–515
Abstract
This paper aims to develop high-order numerical methods for solving the system partial differential equations (PDEs) and partial integro-differential equations (PIDEs) arising in exotic option pricing under regime-switching models and regime-switching jump-diffusion models, respectively. Using cubic Hermite polynomials, the high-order collocation methods are proposed to solve the system PDEs and PIDEs. This collocation scheme has the second-order convergence rates in time and fourth-order rates in space. The computation of the Greeks for the options is also studied. Numerical examples are carried out to verify the high-order convergence and show the efficiency for computing the Greeks.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2019-0119
Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 2 : pp. 497–515
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Option pricing Greeks exotic options Asian options lookback options high-order methods.