Conditioning on One-Step Survival for Barrier Option Simulations

Paul Glasserman () and Jeremy Staum ()
Additional contact information
Paul Glasserman: Graduate School of Business, Columbia University, New York, New York 10027
Jeremy Staum: 226 Rhodes Hall, Cornell University, Ithaca, New York 14853

Operations Research, 2001, vol. 49, issue 6, 923-937

Abstract: Pricing financial options often requires Monte Carlo methods. One particular case is that of barrier options, whose payoff may be zero depending on whether or not an underlying asset crosses a barrier during the life of the option. This paper develops variance reduction techniques that take advantage of the special structure of barrier options, and are appropriate for general simulation problems with similar structure. We use a change of measure at each step of the simulation to reduce the variance arising from the possibility of a barrier crossing at each monitoring date. The paper details the theoretical underpinnings of this method, and evaluates alternative implementations when exact distributions conditional on one-step survival are available and when not available. When these one-step conditional distributions are unavailable, we introduce algorithms that combine change of measure and estimation of conditional probabilities simultaneously. The methods proposed are more generally applicable to terminal reward problems on Markov processes with absorbing states.

Keywords: Simulation; efficiency: Variance reduction; Finance; asset pricing: Computational methods (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (16)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:49:y:2001:i:6:p:923-937

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