Pricing Basket Spread Option Under The Multidimensional Correlated Skew Brownian Motions: An Analytical Approximation Approach

Abstract

In this paper, we propose synthetic analytical approximate pricing formulas for basket and basket spread options within a multidimensional correlated skew Brownian motion framework. For basket options, we derive two analytical approximate pricing formulas by utilizing the partial exact approximation, moment matching method and convex bounds approximation together and achieve accurate and analytical approximations. For basket spread options, we derive a lower bound approximation using the Bjerksund-Stensland-type approach. Numerical examples demonstrate superior performance with consistent robustness and high precision of our formulas, remarkably maintaining excellent performance for highdimensional options. We also note that these approximate pricing formulas can serve as powerful control variates for the variance reduction of Monte Carlo simulations.

Keywords: Option Pricing, Basket Spread Option, Skew Brownian Motion, Analytical Approximation