On Pricing of Discrete Asian and Lookback Options under the Heston Model

TL;DR

This paper introduces a data-driven neural network-based method for efficiently pricing discrete Asian and Lookback options under the Heston model, significantly reducing computational time while maintaining high accuracy.

Contribution

It extends previous work by applying neural networks and stochastic collocation to price complex options under the Heston model efficiently.

Findings

Achieves up to thousands of times faster pricing than classical Monte Carlo methods.

Provides semi-analytic formulas for option pricing under the Heston model.

Demonstrates high accuracy in pricing discrete Asian and Lookback options.

Abstract

We propose a new, data-driven approach for efficient pricing of - fixed- and float-strike - discrete arithmetic Asian and Lookback options when the underlying process is driven by the Heston model dynamics. The method proposed in this article constitutes an extension of our previous work, where the problem of sampling from time-integrated stochastic bridges was addressed. The model relies on the Seven-League scheme, where artificial neural networks are employed to "learn" the distribution of the random variable of interest utilizing stochastic collocation points. The method results in a robust procedure for Monte Carlo pricing. Furthermore, semi-analytic formulae for option pricing are provided in a simplified, yet general, framework. The model guarantees high accuracy and a reduction of the computational time up to thousands of times compared to classical Monte Carlo pricing schemes.