A continuity correction for discrete barrier options

The payoff of 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 Tbe correction shifts the barrier away from the underlying by a factor of exp(beta sigma root Delta t), where beta approximate to 0.5826, sigma is the underlying volatility, and Delta t is the rime between monitoring instants. The correction is justified both theoretically and experimentally.