Sticky Strike and Sticky Delta for Daily Volatility Surface Updates

Article Quant Q&A · Author: John Doe

Summary

This note explains two assumptions desks use to update an implied volatility surface between full calibrations. Under sticky strike, implied volatility stays fixed for each strike as the underlying price changes. An option at a given strike is therefore repriced using the same volatility, even though its moneyness changes. Under sticky delta, volatility is instead tied to an option’s delta or moneyness, so a spot move changes which point on the calibrated surface applies to a fixed-strike option.

The examples describe how a rally shifts an option’s moneyness and how that affects the volatility used for repricing. The note also says these assumptions inform risk calculations such as delta and vega, and that desks may use proxies or interpolation when refreshing surfaces less frequently. It offers no empirical comparison or rule that determines which assumption is best; the appropriate choice depends on the market and the desk’s modeling purpose.

Key ideas

Sticky strike holds implied volatility constant at each strike when spot changes.
Sticky delta holds the surface shape constant by delta or moneyness, so a fixed-strike option can move to a different volatility point.
The two assumptions produce different repricing and risk estimates after a spot move.
Proxy quotes and interpolation may be needed when market data is too sparse for daily recalibration.

Tags

Options Volatility Derivatives pricing Risk management

Full text

# Marking implied vol surface daily with sticky strike and sticky delta

Suppose that implied vol surfaces are calibrated once per month due to data restrictions (i.e. option data is only available at month end). How can a trading desk remark their vol surfaces on a daily basis by only observing the spot and time to maturity? I have heard of techniques such as sticky delta and sticky strike. How do those techniques work? When would one use one technique over the other?

## Answer by Jared (score 1, accepted)

https://quant.stackexchange.com/a/38828

These are introduced in the GS Note on Volatility Regimes. Oversimplifying (a good amount) they say that the surface will look the same based on strike or delta.

E.g.: sticky strike- if your spot price is 100 and the 80 put is trading at 20% volatility according to your surface, you will re-calculate the put price at 20% volatility with your new spot price (the vol per strike has not changed, even though the spot price and therefore the option price has). Sticky delta (more robust) would change the computation to include the new moneyness level, so after a 10 pt rally in spot would have reduced from 80% moneyness to 72%, so you would calculate the option price with your calibrated surface's 72% moneyness vol level.

## Answer by Dora (score 0)

https://quant.stackexchange.com/a/38888

I am working in a trading desk. We don't construct volatility surfaces daily for small-medium entities, but instead, refreshing them in several days. You may need to use proxy and interpolation to estimate quotes first. Sticky strike and sticky delta are the assumption for risk calculation, such as delta and vega.

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