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

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 c...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2016-01, Vol.71 (1), p.443-458
Main Authors: Dang, Duy-Minh, Nguyen, Duy, Sewell, Granville
Format: Article
Language:English
Subjects:
Approximation
Asian
Asian options
Complex systems
Computer simulation
Construction
Jump–diffusion
Mathematical analysis
Mathematical models
Parallel computing
Pricing
Regime-switching
System of partial integro-differential equations
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Summary: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.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2015.12.017