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Abstract:
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Managing the market risk in even plain vanilla financial derivatives transactions is an important concern, for market makers in these products. We recall an option's delta, as suggested by the famous Black-Scholes European option pricing formula. What assumptions are required for an option's delta to be a useful hedge ratio? We discuss the practical limitations on dynamic replication, in particular. As an alternative, we present the problem of option hedging as a statistical decision. This perspective is flexible and can be generalized to address many of the practical concerns with the Black-Scholes delta. Through simulation we compare hedging strategies based on statistical techniques, the Black-Scholes formula, and a couple of ad hoc procedures.
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