Pricing and Deltas of Discretely-Monitored Barrier Options Using Stratified Sampling on the Hitting-Times to the Barrier
25 Pages Posted: 30 Jul 2009
Date Written: July 30, 2009
We develop new Monte Carlo techniques based on stratifying the stock's hitting-times to the barrier for the pricing and Delta calculations of discretely-monitored barrier options using the Black-Scholes model. We include a new algorithm for sampling an Inverse Gaussian random variable such that the sampling is restricted to a subset of the sample space. We compare our new methods to existing Monte Carlo methods and find that they can substantially improve convergence speeds.
Keywords: first-hitting time, passage times, hitting-times, barrier, discretely-monitored, inverse Gaussian, stratified sampling, Monte-Carlo
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