Density functions in high-dimensional basket options

TL;DR

This paper introduces a new approximation method for density functions in high-dimensional basket options, leveraging a generalized Nyquist-Whitakker-Kotel'nikov-Shannon theorem, with proven exponential convergence rates.

Contribution

The paper develops a novel approximation technique for density functions in high-dimensional basket options using advanced sampling theory.

Findings

The method achieves exponential convergence in various scenarios.

It effectively approximates density functions in complex multi-asset derivatives.

The approach is grounded in a generalized sampling theorem.

Abstract

We consider an important class of derivative contracts written on multiple assets (so-called spread options) which are traded on a wide range of financial markets. The present paper introduces a new approximation method of density functions arising in high-dimensional basket options which is based on applications of generalised Nyquist-Whitakker-Kotel'nikov-Shannon theorem we established. It is shown that the method of approximation we propose has an exponential rate of convergence in various situations.