Efficient Pricing of Barrier Options on High Volatility Assets using Subset Simulation

TL;DR

This paper introduces a new stochastic simulation method for pricing barrier options that outperforms traditional Monte Carlo techniques, especially in high volatility scenarios, with confirmed efficiency through extensive simulations.

Contribution

A novel stochastic simulation approach for barrier option pricing that improves efficiency over standard methods, particularly under high volatility conditions.

Findings

Outperforms standard Monte Carlo in efficiency

More effective than multilevel Monte Carlo for certain cases

Confirmed by extensive simulation results

Abstract

Barrier options are one of the most widely traded exotic options on stock exchanges. In this paper, we develop a new stochastic simulation method for pricing barrier options and estimating the corresponding execution probabilities. We show that the proposed method always outperforms the standard Monte Carlo approach and becomes substantially more efficient when the underlying asset has high volatility, while it performs better than multilevel Monte Carlo for special cases of barrier options and underlying assets. These theoretical findings are confirmed by numerous simulation results.