Conditional sampling for barrier option pricing under the Heston model

TL;DR

This paper introduces a quasi-Monte Carlo algorithm for efficient and unbiased pricing of barrier options under the Heston stochastic volatility model, using conditional sampling and modified LT methods.

Contribution

It develops a novel conditional sampling technique that improves barrier option pricing under the Heston model by modifying the LT method to reduce variance and ensure positive payouts.

Findings

Method is unbiased and outperforms unconditional algorithms.

Numerical results demonstrate improved efficiency and accuracy.

Conditioning effectively enforces barrier and payout conditions.

Abstract

We propose a quasi-Monte Carlo algorithm for pricing knock-out and knock-in barrier options under the Heston (1993) stochastic volatility model. This is done by modifying the LT method from Imai and Tan (2006) for the Heston model such that the first uniform variable does not influence the stochastic volatility path and then conditionally modifying its marginals to fulfill the barrier condition(s). We show this method is unbiased and never does worse than the unconditional algorithm. Additionally the conditioning is combined with a root finding method to also force positive payouts. The effectiveness of this method is shown by extensive numerical results.