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

Abstract

Traditional Black-Scholes delta do not minimize variance of hedging risk since there exists a long run negative relationship between implied volatility and underlying price. This paper presents a two-step empirical approach of option delta hedging in which the hedging ratio is determined by volatility-price relationship. 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 can capture the dependency of hedging ratio on volatility-price 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 results in higher hedging gain than related methods appeared in recent works.