Efficient Pricing of Barrier Options on High Volatility Assets using Subset Simulation
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Barrier options are one of the most widely traded exotic options on stock exchanges. They tend to be cheaper than the corresponding vanilla options and better represent investor's beliefs, but have more complicated payoffs. This makes pricing barrier options an important yet non-trivial computational problem. 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.
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