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...
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| Format: | Article |
| Language: | English |
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Allameh Tabataba'i University Press
2021-03-01
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| Series: | Mathematics and Modeling in Finance |
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| Online Access: | https://jmmf.atu.ac.ir/article_12255_953408dc2d9a5f138ee6c6a4f57f137e.pdf |
| _version_ | 1797386690722004992 |
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| author | Parisa Karami Ali Safdari |
| author_facet | Parisa Karami Ali Safdari |
| author_sort | Parisa Karami |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T22:13:58Z |
| format | Article |
| id | doaj.art-294c5cb3dcad4fafb144078dd4f9fafb |
| institution | Directory Open Access Journal |
| issn | 2783-0578 2783-056X |
| language | English |
| last_indexed | 2024-03-08T22:13:58Z |
| publishDate | 2021-03-01 |
| publisher | Allameh Tabataba'i University Press |
| record_format | Article |
| series | Mathematics and Modeling in Finance |
| spelling | doaj.art-294c5cb3dcad4fafb144078dd4f9fafb2023-12-19T05:14:54ZengAllameh Tabataba'i University PressMathematics and Modeling in Finance2783-05782783-056X2021-03-0111697310.22054/jmmf.2021.56261.101812255Finite difference method for basket option pricing under Merton modelParisa Karami0Ali Safdari1Department of Matematics, Allameh Tabataba`i University,Tehran, IranDepartment of Mathematics, Allameh Tabataba'i UniversityIn 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.https://jmmf.atu.ac.ir/article_12255_953408dc2d9a5f138ee6c6a4f57f137e.pdfmerton modelstochastic differential equationsblack-scholes equationbrownian motion |
| spellingShingle | Parisa Karami Ali Safdari Finite difference method for basket option pricing under Merton model Mathematics and Modeling in Finance merton model stochastic differential equations black-scholes equation brownian motion |
| title | Finite difference method for basket option pricing under Merton model |
| title_full | Finite difference method for basket option pricing under Merton model |
| title_fullStr | Finite difference method for basket option pricing under Merton model |
| title_full_unstemmed | Finite difference method for basket option pricing under Merton model |
| title_short | Finite difference method for basket option pricing under Merton model |
| title_sort | finite difference method for basket option pricing under merton model |
| topic | merton model stochastic differential equations black-scholes equation brownian motion |
| url | https://jmmf.atu.ac.ir/article_12255_953408dc2d9a5f138ee6c6a4f57f137e.pdf |
| work_keys_str_mv | AT parisakarami finitedifferencemethodforbasketoptionpricingundermertonmodel AT alisafdari finitedifferencemethodforbasketoptionpricingundermertonmodel |