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Finite difference method for basket option pricing under Merton model | ||
| Journal of Mathematics and Modeling in Finance | ||
| دوره 1، شماره 1، خرداد 2021، صفحه 49-52 اصل مقاله (156.4 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 | ||
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[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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