Document Type : Research Article
Authors
1 Department of Matematics, Allameh Tabataba`i University,Tehran, Iran
2 Department of Mathematics, Allameh Tabataba'i University
Abstract
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.
Keywords
[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.
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