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A Continuity Correction for Discrete Barrier Options

Mark Broadie, Paul Glasserman, Shing-Gang Kou

Publication type: Journal article

Research Archive Topic: Business Economics and Public Policy, Capital Markets and Investments, Risk Management

Abstract

The payoff of a barrier option depends on whether or not a specified asset price, index, or rate reaches a specified level during the life of the option. Most models for pricing barrier options assume continuous monitoring of the barrier; under this assumption, the option can often be priced in closed form. Many (if not most) real contracts with barrier provisions specify discrete monitoring instants; there are essentially no formulas for pricing these options, and even numerical pricing is difficult. We show, however, that discrete barrier options can be priced with remarkable accuracy using continuous barrier formulas by applying a simple continuity correction to the barrier. The correction shifts the barrier away from the underlying by a factor of exp(beta*sigma*sqrt(dt)), where beta approx 0.5826, sigma is the underlying volatility, and dt is the time between monitoring instants. The correction is justified both theoretically and experimentally.
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Citation

Broadie, Mark, Paul Glasserman, and S. G. Kou. "A Continuity Correction for Discrete Barrier Options." Mathematical Finance 7, no. 4 (1997): 325-49.


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