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

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.