Conditional sampling for barrier option pricing under the LT method

TL;DR

This paper introduces a conditional sampling scheme for barrier option pricing under the LT method, achieving significant variance reduction and extending to knock-in options with a root-finding approach, supported by numerical evidence.

Contribution

The paper presents a novel conditional sampling method for barrier options under the LT algorithm, enhancing variance reduction and extending applicability to knock-in options.

Findings

Substantial variance reduction compared to existing methods

Effective extension to knock-in barrier options

Numerical results confirm improved efficiency

Abstract

We develop a conditional sampling scheme for pricing knock-out barrier options under the Linear Transformations (LT) algorithm from Imai and Tan (2006). We compare our new method to an existing conditional Monte Carlo scheme from Glasserman and Staum (2001), and show that a substantial variance reduction is achieved. We extend the method to allow pricing knock-in barrier options and introduce a root-finding method to obtain a further variance reduction. The effectiveness of the new method is supported by numerical results.