# Array-RQMC for option pricing under stochastic volatility models

## TL;DR

This paper explores the application of Array-RQMC to stochastic volatility models for option pricing, demonstrating significant variance reduction and effectiveness across various complex models.

## Contribution

It extends Array-RQMC techniques to stochastic volatility models, showing their effectiveness despite higher-dimensional challenges.

## Key findings

- Array-RQMC significantly reduces variance in stochastic volatility models.
- The method is effective for variance-gamma, Heston, and Ornstein-Uhlenbeck models.
- Numerical results confirm the practical benefits of the approach.

## Abstract

Array-RQMC has been proposed as a way to effectively apply randomized quasi-Monte Carlo (RQMC) when simulating a Markov chain over a large number of steps to estimate an expected cost or reward. The method can be very effective when the state of the chain has low dimension. For pricing an Asian option under an ordinary geometric Brownian motion model, for example, Array-RQMC reduces the variance by huge factors. In this paper, we show how to apply this method and we study its effectiveness in case the underlying process has stochastic volatility. We show that Array-RQMC can also work very well for these models, even if it requires RQMC points in larger dimension. We examine in particular the variance-gamma, Heston, and Ornstein-Uhlenbeck stochastic volatility models, and we provide numerical results.