Measuring Option Skew with Delta Risk Reversals and Volatility Points
Summary
The discussion compares possible ways to track changes in option volatility skew relative to at-the-money volatility. One answer proposes measuring the implied-volatility difference between the strikes where Black–Scholes d2 equals zero and d1 equals zero. It argues that these points coincide under a symmetric smile, while the d1-zero point is more sensitive to correlation and the d2-zero point is linked to the volatility-swap strike and the midpoint of the lognormal distribution.
Another answer notes that skew is commonly quoted through delta risk reversals, particularly at 10% and 25% delta in foreign exchange markets. It recommends monitoring absolute changes in risk reversals. These are practitioner viewpoints, not a universal standard: the first contributor explicitly presents a personal preference and says a sensitivity claim is unproven, while the second refers to FX quoting conventions. The suitable metric depends on the market and quoting framework.
Key ideas
- One proposed skew measure is the implied-volatility difference between the d2-zero and d1-zero strikes.
- The d2-zero point is described as less sensitive to correlation and related to the volatility-swap strike.
- Delta risk reversals are a common skew quotation, especially in foreign exchange markets.
- One contributor favors absolute changes in risk reversals for tracking skew over time.
- The discussion offers preferences and conventions rather than an accepted universal measure.
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Full text
# What are popular metrics for Option Skew? # What are popular metrics for Option Skew? What are popular metrics to track skew? Would it be the difference between OTM option and ATM option IV? Would it be a percentage difference in IV? Also, if both are valid, would a % change be better or absolute change be better? My goal is to track how skew changes over time, obviously in relation to ATM volatility. Thanks! ## Answer by user34971 (score 7) https://quant.stackexchange.com/a/49979 My preferred measure for skew would be the difference between the implied volatilities corresponding to the strikes where the Black-Scholes $d_2 = 0$ and $d_1 = 0$. The reason I prefer this to others you often come across is that when the smile is symmetric the $d_2=0$ implied volatility equals the $d_1 = 0$ implied volatility. Furthermore, the implied volatility corresponding to $d_2=0$ is quite insensitive to correlation, whereas the $d_1 = 0$ implied volatility is very sensitive to correlation. Also, the $d_2=0$ implied volatility is related to the volatility swap strike and corresponds to the the mid-point of the Black-Scholes log-normal distribution. Hence in a sense you can regard the $d_2=0$ strike as the pivot point about which the skew "rotates" as correlation changes, and correlation of course impacts skewness. But as far as I know there is no generally accepted measure for skew, I am just giving my opinion. EDIT: I suspect even that the $d_1 = 0$ implied volatility is the most correlation sensitive point on the skew, but I cannot prove that (yet). ## Answer by Xman (score 5) https://quant.stackexchange.com/a/49987 Volatility Skew is generally quoted in terms of Risk Reversals. I know that for FX products and because of Delta stickiness, the quoted Risk reversals are regarding the 10% and 25% Delta. Edit: To complete my answer, Skew results from a difference in terms of offer and demand for Calls/Puts. So the best way to track its changes over time would be by an absolute change of Risk Reversals. This absolute change is for instance what the Fundamental Review Of the Trading Book (FRTB) requires to monitor...
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