A Generalized Bachelier Formula for Pricing Basket and Spread Options

Abstract

In this paper we propose a closed-form pricing formula for European basket and spread options. Our approach is based on approximating the risk-neutral probability density function of the terminal value of the basket using a Gauss-Hermite series expansion around the Gaussian density. The new method is quite general as it can be applied for a basket with a large number of assets and for all dynamics where the joint characteristic function of log-returns is known in closed form. We provide a simulation study to show the accuracy and the speed of our methodology.

Keywords: Basket options, Spread options, Option pricing, Gauss-Hermite series expansion

JEL Classification: C63, G13