Title: 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.