Estimating Option-Implied Skewness and Kurtosis from Volatility Surfaces

Summary

The document asks whether public sources provide option-implied skewness and kurtosis, especially for European equity indices, and explains why the researcher is seeking an alternative measure: their computed kurtosis is unstable for use in regression, while skewness is more stable. It mentions the CBOE SKEW index as an example of a public measure, but the text supplies no answer identifying data vendors or sources.

The described calculation fits a spline or polynomial to implied volatility across moneyness, converts the fitted volatilities into a risk-neutral density using the Breeden-Litzenberger relationship, and derives probabilities from that density. Uniform draws are then mapped through the cumulative distribution to moneyness values, whose sample moments give skewness and kurtosis. The researcher attributes the kurtosis instability to this sampling and inverse-CDF mapping step. No empirical comparison, diagnosis of the instability, or validation against an alternative estimator is provided.

Key ideas

• The proposed workflow estimates a risk-neutral density from an implied-volatility curve using the Breeden-Litzenberger relationship.
• The density is converted to a cumulative distribution, which is used to map uniform draws to moneyness values.
• Skewness and kurtosis are calculated from the resulting sample of moneyness values.
• The researcher reports that kurtosis is unstable in their implementation, particularly around the inverse-CDF mapping step.
• The document asks about public data sources but does not provide a source recommendation or validate the calculation.

Tags

# Are there publicly available measures of option-implied skewness and kurtosis?


# Are there publicly available measures of option-implied skewness and kurtosis?












As mentioned in the title, are there publicly available measures of option-implied skewness and kurtosis? (that represent the skewness and kurtosis of the option-implied risk-neutral distribution, preferably for European stock indices) Something like the CBOE SKEW index.

Some examples of data sources that could contain them might be Bloomberg, Yahoo Finance, WRDS etc.

EDIT.

The reason I am asking this is because my own measured option-implied kurtosis is unstable, which makes it infeasible to be used in a regression. Option-implied skewness is still stable, so a publicly available measure is not that high a priority as compared to kurtosis.

MY CALCULATION FOR SKEWNESS AND KURTOSIS

- Obtain a set of implied vols (per moneyness K/S) and fit spline/polynomial; discretize vol skew appropriately.

- Convert all IVs (from the spline) to RNDs via Breeden-Litzenberger closed-form solution.

- With the set of RNDs, convert it to risk-neutral probabilities (basically PDF to CDF).

- Generate a set of uniform random variables (URVs, bounded by 0 to 1) to simulate a data sample (the larger the set of URVs, the more accurate the measurement of skewness and kurtosis).

- Using the set of URVs, find the one-to-one match with the CDF and the appropriate K/S.

- Calculate the skewness and kurtosis across the set of derived K/S.

It is because of step (5.) that causes the instability of option-implied kurtosis.

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.