Skew Stickiness Ratio and Volatility Smile Dynamics

Summary

The document introduces the skew stickiness ratio (SSR) as a way to describe how at-the-money-forward implied volatility responds when the underlying asset moves. It uses this measure to distinguish two common smile-dynamics assumptions. Under sticky strike, implied volatilities at fixed strikes near the money stay approximately unchanged as spot moves, so the at-the-money-forward point shifts along the smile; this corresponds to SSR equal to one. Under sticky delta, the smile shifts with spot while volatility at fixed log-moneyness remains unchanged, corresponding to SSR equal to zero.

The response recommends Lorenzo Bergomi’s work on smile dynamics as a technical treatment and notes that it classifies stochastic-volatility models by their SSR behavior. This gives a quantitative framework for comparing model-implied smile responses, but the document does not describe how to detect transitions between regimes in historical data. Nor does it present an empirical transition study, calibration procedure, or trading test. SSR is therefore offered here as a useful measure of dynamics, not as a complete method for identifying when market behavior changes.

Key ideas

• The skew stickiness ratio measures at-the-money-forward volatility movement conditional on an underlying move.
• Sticky strike corresponds to an SSR of one, with fixed-strike implied volatilities near the money remaining stable.
• Sticky delta corresponds to an SSR of zero, with the smile translating alongside spot.
• Stochastic-volatility models can be compared by their implied SSR behavior.
• The document does not provide a method for detecting historical transitions between regimes.

Tags

# Transition Between Volatility Regimes


# Transition Between Volatility Regimes












Emanuel Derman wrote a great paper in 1999 about volatility regimes and the adjustments the market makes during these periods (sticky strike, sticky implied tree, sticky delta, etc).

Has any research been done on the transitions between these regimes, even if identifying them retroactively?

## Answer by Olórin (score 8)

https://quant.stackexchange.com/a/33505

I don't know about sticky implied tree, but for sticky strike and sticky implied delta the classification is not that dead end as onlyvix.blogspot.com might think. Look at Lorenzo Bergomi's Smile Dynamics IV paper. He defines the skew stickiness ratio SSR which roughly quantifies how much the ATMF volatility moves conditional on a move of the underlying.

- The sticky-strike regime corresponds to SSR = 1 : as the spot moves, implied volatilities for fixed strikes near the money stay frozen – the ATMF volatility slides along the smile.

- The sticky-delta regime corresponds to SSR = 0. The whole smile experiences a translation alongside the spot: volatilities for fixed log-moneyness are frozen.

The paper is a bit technical but worth reading as he classifies stochastic volatility models according to SSR's.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.