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

37 Pages Posted: 24 Nov 2020 Last revised: 19 Apr 2021

See all articles by Peng Zhu

Peng Zhu

Nanjing University

Kun Xia

HKUST Business School

Xuewei Yang

Nanjing University - School of Management and Engineering

Date Written: October 8, 2020


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.

Keywords: Option; Delta hedging; Dynamic of volatility-price elasticity; Risk management; Minimum variance

JEL Classification: G13

Suggested Citation

Zhu, Peng and Xia, Kun and Yang, Xuewei, Delta Hedging and Volatility-Price Elasticity: A Two-Step Approach (October 8, 2020). Available at SSRN: or

Peng Zhu

Nanjing University ( email )

Nanjing, Jiangsu 210093

Kun Xia

HKUST Business School ( email )

Clearwater Bay
Kowloon, 999999
Hong Kong

Xuewei Yang (Contact Author)

Nanjing University - School of Management and Engineering ( email )

22 Hankou Road, Gulou District
Nanjing, Jiangsu 210093

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