Hedging exotic options: theory and risks

This study examines hedging strategies for exotic options and assesses the behavior of the Greeks of these options from a risk management perspective. Normal discrete dynamic hedging is extended to a strategy where a certain limit is posed on the Delta exposure. The exotic option types discussed are binary, barrier and Asian options. Exotic options have more difficult risk patterns around limit situations such as near expiration, strike or at the barrier level. Dynamic hedging may therefore not be feasible for these option types and we well therefore also consider static hedging strategies. The dynamic and static hedging strategies are assessed using simulation in a Black-Scholes setting, and later under a Heston-type dynamics of the volatility. The research shows that for some option types dynamic hedging yields favorable results, whereas other options are best replicated using static strategies. While this is highly related to the behavior of the Greeks, another concern is that a perfect replication is in general not possible and a trade-off has to be made.