Theory and construction of Quasi-Monte Carlo rules for option pricing and density estimation

TL;DR

This paper introduces a novel Quasi-Monte Carlo method for efficiently estimating Asian option prices, distribution functions, and densities by combining preintegration with tailored lattice rules for improved accuracy.

Contribution

It proposes a new approach that integrates preintegration with customized lattice Quasi-Monte Carlo rules for better option pricing and density estimation.

Findings

Enhanced accuracy in Asian option pricing

Effective density and distribution function estimation

Improved convergence properties of the method

Abstract

In this paper we propose and analyse a method for estimating three quantities related to an Asian option: the fair price, the cumulative distribution function, and the probability density. The method involves preintegration with respect to one well chosen integration variable to obtain a smooth function of the remaining variables, followed by the application of a tailored lattice Quasi-Monte Carlo rule to integrate over the remaining variables.