Delta Hedging and Volatility-Price Elasticity: A Two-Step Approach

Abstract

Black-Scholes delta does not minimize variance of hedging risk since it fails to capture the long run negative relationship between implied volatility and underlying price. Existing works have successfully seized the aforementioned long run relationship and improved the hedging performance. We move one step further by incorporating the short-term properties of the volatility-price relationship via a two-step empirical approach. Specifically, we find that the dependency of minimum variance (MV) hedging ratio on volatility-price elasticity is quite stable and that the volatility-price elasticity exhibits characteristic of mean-reverting. Therefore we first estimate a model which captures the dependency of hedging ratio on volatilityprice elasticity, and then substitute predictions of future volatility-price elasticity into the pre-fixed model to obtain the MV hedging ratio. We test the new approach using the S&P 500 daily option data and show that our approach improves hedging performance over related methods appeared in recent works.