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Karami, Parisa, Safdari, Ali. (1399). Finite difference method for basket option pricing under Merton model. سامانه مدیریت نشریات علمی, 1(1), 69-73. doi: 10.22054/jmmf.2021.56261.1018
Parisa Karami; Ali Safdari. "Finite difference method for basket option pricing under Merton model". سامانه مدیریت نشریات علمی, 1, 1, 1399, 69-73. doi: 10.22054/jmmf.2021.56261.1018
Karami, Parisa, Safdari, Ali. (1399). 'Finite difference method for basket option pricing under Merton model', سامانه مدیریت نشریات علمی, 1(1), pp. 69-73. doi: 10.22054/jmmf.2021.56261.1018
Karami, Parisa, Safdari, Ali. Finite difference method for basket option pricing under Merton model. سامانه مدیریت نشریات علمی, 1399; 1(1): 69-73. doi: 10.22054/jmmf.2021.56261.1018

Finite difference method for basket option pricing under Merton model

Journal of Mathematics and Modeling in Finance
دوره 1، شماره 1، خرداد 2021، صفحه 69-73    اصل مقاله (122.41 K)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.22054/jmmf.2021.56261.1018
نویسندگان
Parisa Karami* 1؛ Ali Safdari2
1Department of Matematics, Allameh Tabataba`i University,Tehran, Iran
2Department of Mathematics, Allameh Tabataba'i University
چکیده
In financial markets , dynamics of underlying assets are often specified via stochastic
differential equations of jump - diffusion type . In this paper , we suppose that two financial
assets evolved by correlated Brownian motion . The value of a contingent claim written on two
underlying assets under jump diffusion model is given by two - dimensional parabolic partial
integro - differential equation ( P I D E ) , which is an extension of the Black - Scholes equation with
a new integral term . We show how basket option prices in the jump - diffusion models , mainly
on the Merton model , can be approximated using finite difference method . To avoid a dense
linear system solution , we compute the integral term by using the Trapezoidal method . The
numerical results show the efficiency of proposed method .
Keywords: basket option pricing, jump-diffusion models, finite difference method.
کلیدواژه‌ها
Merton model؛ stochastic differential equations؛ Black-Scholes equation؛ Brownian motion
مراجع
[1] F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Polit. Econ., 81 (3) (1973), 637{144.
[2] R. Merton, Option pricing when underlying stock returns are discontinuous, Journal of Financial Economics, 3 (1976), 125{144.
[3] S. S. Clift and P. A. Forsyth, Numerical solution of two asset jump diffusion models for options valuation, Appl. Numer. Math., 58 (2008), 743{782.

[4] Y. d'Halluin, P. A. Forsyth, and K. R. Vetzal, Robust numerical methods for contingent claims under jump diffusion processes, Journal of IMA Journal of Numerical Analysis, 25 (1) (2005), 87{112.

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