Radial Basis Function Approximation Method for Pricing of Basket Options Under Jump Diffusion Model

Abstract

Option contracts under actual market conditions which are more complex than a simple Black-Scholes model are important hedging strategies in the modern financial market. Basket options are attractive products which required the reliable pricing method to take all the beneficial characteristics of a basket option such as correlation effect of underlying assets. The focus of this paper is to present the radial basis function partition of unity method (RBF–PUM) for evaluation of basket options in which underlying assets price follow the Merton jump diffusion model. Numerical experiments are performed for the resulting partial integro-differential equation (PIDE). The resulting valuation method allow for an adaptive space discretization in region near the exercise price to reduce computational cost. The domain truncation effects on the computational error is investigated for the proposed numerical approach. Our numerical examples with two and three underlying assets show that the proposed scheme is accurate, capability of local adaptivity, and efficient in comparison of alternative methods for accurate option prices.