Discrete Partial Barrier Options with a Moving Barrier

Abstract

Barrier options come in many forms. In this article we study the pricing of discrete partial barrier options where the barrier level may change deterministically during the monitoring period and monitoring takes place at not-necessarily equally spaced points in time. We provide closed-form pricing formulas for the prices of these options in a Black-Scholes (1973) world. Using these results, we show that monitoring the reference index discretely instead of continuously may have a very significant effect on the prices of barrier options.

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