Estimating Option-Implied Skewness and Kurtosis Across Expirations

Summary

The document asks how to estimate skewness and kurtosis implied by a daily cross-section of call and put options. The described data fields include delta, strike, volume, and spot price, with multiple options and potentially multiple expiration dates on the same day. It raises the practical question of whether to estimate the measures using all expirations together or to handle each maturity separately.

The post does not provide a calculation procedure, R implementation, dataset, or empirical result. An edit points readers toward the Corrado and Su model and corrected equations attributed to Brown and Robinson as possible approaches. It offers these as suggestions rather than demonstrating their use, and leaves choices about maturity grouping and the suitability of the available option data unresolved.

Key ideas

• Option-implied skewness and kurtosis are the target measures for a daily options dataset.
• The dataset may contain many puts and calls with different strikes and expirations.
• The post raises whether to pool expirations or estimate the measures by maturity.
• It cites Corrado and Su and corrected equations attributed to Brown and Robinson, but gives no implementation.

Tags

# How to estimate option implied skewness and kurtosis in R


# How to estimate option implied skewness and kurtosis in R












Suppose that i have data that for each day i have more than one option, either put or call. I.E. I have more than 20 put options and 20 call options for each specific day.

What is the way to estimate the option implied skewness and kurtosis for that specific dataset? Is there a package in R, or some code to help me understand how to do it? For each option i have information like the `delta`, `strike price`, `volume`, `spot price`.

Thank you!

EDIT.1: I am not sure in terms of data; typically more than 1 option is present on a certain date. I.e. on the `03-02-2010` we can have 30 options on expiration date `A`, 50 on expiration date `B` and so forth, which each having their respective values introduced prior. When finding the kurtosis/skewness the procedure includes at the same time all options; taking into account the different expiration dates (seems more logical), or not?

EDIT.2: One good way to measure those metrics, is through the Corrado and Su (1996) model, or, even better, with the corrected Brown and Robinson (2002) equations of the Corrado and Su model. Link is in the comment below.

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.