Adaptive numerical integration and control variates for pricing Basket Options

TL;DR

This paper introduces an adaptive numerical integration method with control variates for efficiently pricing multidimensional vanilla options, improving accuracy and computational performance across various dimensions.

Contribution

It presents a novel splitting strategy for adaptive integration and combines it with PCA-based dimension reduction for high-dimensional option pricing.

Findings

Effective in dimensions up to ten

Improves accuracy over existing methods

Reduces computational complexity

Abstract

We develop a numerical method for pricing multidimensional vanilla options in the Black-Scholes framework. In low dimensions, we improve an adaptive integration algorithm proposed by two of the authors by introducing a new splitting strategy based on a geometrical criterion. In higher dimensions, this new algorithm is used as a control variate after a dimension reduction based on principal component analysis. Numerical tests are performed on the pricing of basket, put on minimum and digital options in dimensions up to ten.