Delta hedging and volatility-price elasticity: A two-step approach

We incorporate a time-varying negative relationship for implied volatility and underlying price into the delta hedging problem, where traders aim to minimize the variance of changes in the value of an option position by trading an appropriate amount of the underlying asset. We show that volatility-price elasticity is mean-reverting and embed predictions of the elasticity in a hedge ratio model that incorporates the negative volatility-price relationship. Our tests show that when applied to index options data, the proposed approach improves hedging performance over methods that rely solely on the long-run mean of the volatility-price relationship.