Evidence and References for Skewness and Kurtosis Arbitrage

Summary

The document asks whether traders can find statistically significant arbitrage opportunities by comparing implied and historical higher moments, particularly skewness and kurtosis. It distinguishes this question from better-known volatility arbitrage and frames the issue in the context of research using DAX options, while observing that this market is less liquid than comparable US options markets.

The response does not provide empirical results, a trading method, or evidence that the proposed strategy works. Instead, it points readers to a section on higher-moment bets in a book about dynamic hedging, where the topic is discussed conceptually. That reference may help with background, but it does not answer whether the opportunity has been tested successfully or how liquidity, hedging costs, estimation error, and statistical significance affect results. The document is therefore a research lead rather than a substantiated arbitrage strategy.

Key ideas

• The question concerns trading differences between implied and historical skewness or kurtosis.
• The prompt contrasts higher-moment research with established volatility arbitrage.
• The discussion is framed around DAX options and notes their relative liquidity limitation.
• The response points to conceptual reading but supplies no empirical findings or strategy evaluation.

Tags

# Higher moments arbitrage


# Higher moments arbitrage












Is there concrete evidence that statistical arbitrage (historical vs. implied) on higher moments, specifically skewness and kurtosis, can be (significantly) done?

Working from this source, the author finds clear evidence on volatility arbitrage. Which is mainstream, very well understood, and heavily done (e.g. VIX trading). But, to take the discussion further, this research (Chapter 9 - Trading on Deviations of Implied and Historical Distributions) is specifically addressing this question, applied on DAX data, which is not a as liquid as the equivalent US options markets.

Therefore, my main question is: has anyone done any empirical work on this topic and could relate to it?

## Answer by Karan Pillai (score 2)

https://quant.stackexchange.com/a/31272

I'm not sure if this would qualify as "empirical work" but you should definitely read Dynamic Hedging if you haven't already. Taleb talks a lot about this. To be more specific, have a look at page 264, the section called "Higher Moment Bets". I hope this is helpful, although I am not sure if this is what you are looking for.

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.