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-MinhNguyen, DuySewell, Granville Numerical schemes for pricing Asian options under state-dependent regime-switching jump-diffusion models Computers and Mathematics with Applications   Check publisher's open access policy 1873-76680898-1221 2016-01-01 2015 Article (original research) 10.1016/j.camwa.2015.12.017 Not Open Access 71 1 443 458 16 Kidlington, Oxford, United Kingdom Pergamon Press eng 2611 Modelling and Simulation1703 Computational Theory and Mathematics2605 Computational Mathematics 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. 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. Asian optionsRegime-switchingJumpâ€“diffusionSystem of partial integro-differential equations C1 Provisional Code UQ Published online 29 December 2015

 Document type: Journal Article Article (original research) School of Mathematics and Physics Official 2016 Collection

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