Numerical schemes for pricing Asian options under state-dependent regime-switching jump–diffusion models
| Autor: | Duy-Minh Dang, Duy Nguyen, Granville Sewell |
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| Rok vydání: | 2016 |
| Předmět: |
Scheme (programming language)
Mathematical optimization Constructive proof Jump diffusion Complex system Monotonic function 01 natural sciences 010104 statistics & probability 0502 economics and business Applied mathematics Asian option Asset (economics) Limit (mathematics) 0101 mathematics computer.programming_language Mathematics Coupling 050208 finance Partial differential equation 05 social sciences Process (computing) Regime switching Computational Mathematics Computational Theory and Mathematics Modeling and Simulation Computer Science::Mathematical Software computer |
| Zdroj: | Computers & Mathematics with Applications. 71:443-458 |
| ISSN: | 0898-1221 |
| DOI: | 10.1016/j.camwa.2015.12.017 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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