Finite difference method for basket option pricing under Merton model
In financial markets , dynamics of underlying assets are often specified via stochasticdifferential equations of jump - diffusion type . In this paper , we suppose that two financialassets evolved by correlated Brownian motion . The value of a contingent claim written on twounderlying assets under j...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Allameh Tabataba'i University Press
2021-03-01
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| Series: | Mathematics and Modeling in Finance |
| Subjects: | |
| Online Access: | https://jmmf.atu.ac.ir/article_12255_953408dc2d9a5f138ee6c6a4f57f137e.pdf |
| Summary: | In financial markets , dynamics of underlying assets are often specified via stochasticdifferential equations of jump - diffusion type . In this paper , we suppose that two financialassets evolved by correlated Brownian motion . The value of a contingent claim written on twounderlying assets under jump diffusion model is given by two - dimensional parabolic partialintegro - differential equation ( P I D E ) , which is an extension of the Black - Scholes equation witha new integral term . We show how basket option prices in the jump - diffusion models , mainlyon the Merton model , can be approximated using finite difference method . To avoid a denselinear system solution , we compute the integral term by using the Trapezoidal method . Thenumerical results show the efficiency of proposed method .Keywords: basket option pricing, jump-diffusion models, finite difference method. |
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| ISSN: | 2783-0578 2783-056X |