PRICING AND DELTAS OF DISCRETELY-MONITORED BARRIER OPTIONS USING STRATIFIED SAMPLING ON THE HITTING-TIMES TO THE BARRIER

Mark Joshi () and Robert Tang ()
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Mark Joshi: Centre for Actuarial Studies, University of Melbourne, Victoria, VIC3010, Australia
Robert Tang: Centre for Actuarial Studies, University of Melbourne, Victoria, VIC3010, Australia

International Journal of Theoretical and Applied Finance (IJTAF), 2010, vol. 13, issue 05, 717-750

Abstract: 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 (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219024910005978

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