Using Volatility Surface Regimes to Adjust Option Delta
Summary
The discussion presents four idealized ways an implied-volatility surface may respond when spot moves: sticky delta, sticky strike, sticky local volatility, and jumpy volatility. Each implies a different relationship between spot and implied volatility. Sticky delta is described as having positive spot-volatility correlation, while sticky local volatility and jumpy volatility imply negative correlation, with especially sharp volatility responses in panicked markets. Sticky strike keeps implied volatility fixed for options at the same currency strike.
The practical application is to estimate how the implied volatility of a fixed-strike option may change with spot, then account for that change when interpreting Black-Scholes delta. If implied volatility falls as spot rises, the total price sensitivity includes both the direct spot effect and the vega-weighted volatility effect, so the model’s delta may be biased if volatility is held fixed. The answer offers intuition rather than a calibration procedure or trading evidence; actual surface behavior can vary by market and horizon, so the regimes are idealizations rather than guarantees.
Key ideas
- Volatility surface regimes describe how implied volatility changes as spot moves.
- Sticky strike holds implied volatility constant for options with a fixed currency strike.
- Negative spot-volatility correlation can make a fixed-volatility Black-Scholes delta inaccurate.
- The volatility response contributes to option price sensitivity through vega.
- These regimes are idealized descriptions, not a complete method for forecasting or trading skew.
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# Spot and Vol Correlation in Idealised Regimes of the Volatility Surface # Spot and Vol Correlation in Idealised Regimes of the Volatility Surface From http://www.globalvolatilitysummit.com/wp-content/uploads/2015/10/Santander-Volatility-Trading-Primer-Part-II.pdf it states that there are the four idealised regimes of volatility surface. > 1) Sticky delta (or sticky moneyness). Sticky delta assumes a constant volatility for options of the same strike as a percentage of spot. For example, ATM or 100% strike volatility has constant volatility. As this model implies there is a positive correlation between volatility and spot, the opposite of what is usually seen in the market, it is not a particularly realistic model (except over a very long time horizon). (2) Sticky strike. A sticky strike volatility surface has a constant volatility for options with the same fixed currency strike. Sticky strike is usually thought of as a stable (or unmoving) volatility surface as real-life options (with a fixed currency strike) do not change their implied volatility. (3) Sticky local volatility. Local volatility is the instantaneous volatility of stock at a certain stock price. When local volatility is static, implied volatility rises when markets fall (ie, there is a negative correlation between stock prices and volatility). Of all the four volatility regimes, it is arguably the most realistic and fairly prices skew. (4) Jumpy volatility. We define a jumpy volatility regime as one in which there is an excessive jump in implied volatility for a given movement in spot. There is a very high negative correlation between spot and volatility. This regime usually occurs over a very short time horizon in panicked markets (or a crash). The chapter then goes on to explain the four regimes in more detail, however, I am unclear as to how this can be used in a practical sense? If not, why did the author introduce these regimes? Moreover, it states that skew and the effects of remarking the volatility surface is very different in each regime (see pg 221). Therefore I would have thought it would be very hard to trade skew as you may have to change between the regimes? ## Answer by phubaba (score 2, accepted) https://quant.stackexchange.com/a/32737 In black-scholes world, correlation between volatility and spot is zero. From the above details you can estimate how the implied volatility for a given option (note options have FIXED strikes) might change for a given move in spot. If when stock goes up, the option's implied vol goes down, this would be a violation of the black-scholes model (which scenario 1/2/3/4 would the correlation be negative?). In particular, your black scholes delta will be biased. Given the option's vega, can you tell me in what way the delta would be biased? specifically what is dBS(S, sigma(S))/dS ? where dsigma(s)/ds < 0 This might give you some intuition for how this information would be used in a practical sense.
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