Document Type : Research Article

Authors

• Parisa Karami ¹
• Ali Safdari ²

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

• Merton model
• stochastic differential equations
• Black-Scholes equation
• Brownian motion