The Hedging Costs of Discrete Monitoring of FX Barrier Options

Abstract

The effects of the discrete monitoring of barrier options is analysed. We determine the costs that a market-maker should charge when making prices for such a kind of exotic options. The costs are related to the Delta-hedging activity around the barrier level between two subsequent monitoring dates, by assuming a reasonable hedging rule followed by the trader. We explain how our result is related to an apparently similar result by Becker and Wystup (2005) and finally we present a practical application showing that the inclusion of the Delta-hedging costs has a relevant impact on the discretely monitored barrier options prices.

Keywords: discrete monitored barrier, local time, slippage cost, hedging cost, ecb 37

JEL Classification: G13