Global Quantitative & Derivatives Strategy23 February 2024J P M O R G A Nwww.jpmorganmarkets.comCorrection (first published 22 February 2024) (See disclosures for details)Global Quantitative and Derivatives StrategyLibin Cheng AC(1-212) 270-1434libin.cheng@jpmchase.comPeng Cheng, CFA AC(1-212) 622-5036peng.cheng@jpmorgan.comJ.P. Morgan Securities LLCIn this systematic dispersion update, we want to discuss about the performance impact on the systematic dispersion strategy of hedging through skew delta and the estimation of skew stickiness ratio.Black Scholes delta is a good starting point for hedging the options delta. However, due to the volatility skew, the assumption of flat volatility in Black Scholes world is hardly met in practice. There are a couple of papers discussing how the volatility skew changes when the market moves and the corresponding affects on the pricing and risk management of volatility instruments. Two popular rules are sticky strike and sticky delta. Sticky strike rule assumes that the implied volatility curve will not change if the spot moves, i.e. the volatility skew sticks to the strike price. As a result, BS delta should be used to hedge under this assumption. However, the ATMF vol moves along the original volatility curve when spot moves. Sticky delta (or moneyness) rule assumes that the implied volatility curve will shift horizontally with the spot movement, and preserve the shape in terms of delta (or moneyness); for example, under sticky delta rule, the ATMF vol will be persistent.Figure 1: Change of volatility skew based on sticky strike or sticky delta rules if spot moves down by 10%See page 12 for analyst certification and important disclosures.J.P. Morgan does and seeks to do business with companies covered in its research reports. As a result, investors should be aware that the firm may have a conflict of interest that could affect the objectivity of this report. Investors should consider this report as only a single factor in making their investment decision.Global Equity DerivativesSystematic Dispersion Update2Libin Cheng AC (1-212) 270-1434libin.cheng@jpmchase.comJ.P. Morgan Securities LLCPeng Cheng, CFA AC (1-212) 622-5036peng.cheng@jpmorgan.comGlobal Quantitative & Derivatives StrategyGlobal Equity Derivatives23 February 2024J P M O R G A NThe skew stickiness ratio is introduced to describe the joint dynamic between spot and volatility skew. As introduced in Bergomi 2009, the skew stickiness ratio (SSR) can be defined as:where K=Strike/Spot. As pointed out in the paper, the SSR is 1 and 0 under the sticky strike and sticky delta assumptions, respectively.In addition, it is possible for us to estimate the SSR as the regression coefficient of the change of ATMF vol () on the change of log return of the spot in units of the ATMF skew ().We apply this method to estimate the historical 3m SPX SSR and curren...
