Sum of all Black-Scholes-Merton models: An efficient pricing method for spread, basket, and Asian options

TL;DR

This paper introduces a unified, efficient method for pricing multivariate Black-Scholes-Merton options like basket, spread, and Asian options by expressing prices as quadrature integrations and optimizing the state space rotation.

Contribution

It presents a novel approach that overcomes the curse of dimensionality, enabling accurate and efficient pricing of complex multi-asset options.

Findings

Method achieves high accuracy with fewer quadrature nodes.

Significant computational efficiency improvements demonstrated.

Applicable to various multivariate option types.

Abstract

Contrary to the common view that exact pricing is prohibitive owing to the curse of dimensionality, this study proposes an efficient and unified method for pricing options under multivariate Black-Scholes-Merton (BSM) models, such as the basket, spread, and Asian options. The option price is expressed as a quadrature integration of analytic multi-asset BSM prices under a single Brownian motion. Then the state space is rotated in such a way that the quadrature requires much coarser nodes than it would otherwise or low varying dimensions are reduced. The accuracy and efficiency of the method is illustrated through various numerical experiments.