The Skewness and Kurtosis of European Options and the Implications for Trade Sizing

13 Pages Posted: 21 Apr 2017

See all articles by Euan Sinclair

Euan Sinclair

FactorWave; Bluefin Trading

Reuben Brooks

University of Virginia

Date Written: April 20, 2017

Abstract

Long vanilla call option positions have unlimited profit potential and limited loss potential, and the opposite is true for short call option positions. Long vanilla puts do not have unlimited profit potential but, for commonly traded strikes, the maximum profit of a long put will be far greater than the maximum loss (the premium of the option). Again, the opposite is true for short put positions: their maximum loss is far greater than the potential gain. Equivalently, option returns are highly skewed and kurtotic. In this note, we calculate the skewness and kurtosis for European calls and puts. Next, using a power series expansion, we derive a simple approximation to the Kelly fraction for optimal trade sizing when returns are non-normal. Taken together, these two results are used to show that the higher order moments of option positions have an economically significant effect on optimal trade sizing when using the Kelly criterion.

Keywords: options, skewness, kurtosis, Kelly criterion, optimal growth

JEL Classification: D81, G10, G11, G13

Suggested Citation

Sinclair, Euan and Brooks, Reuben, The Skewness and Kurtosis of European Options and the Implications for Trade Sizing (April 20, 2017). Available at SSRN: https://ssrn.com/abstract=2956161 or http://dx.doi.org/10.2139/ssrn.2956161

Euan Sinclair (Contact Author)

FactorWave ( email )

CHICAGO, IL 60647
United States

HOME PAGE: http://www.factorwave.com

Bluefin Trading ( email )

440 South LaSalle
Suite 900
Chicago, IL 60605
United States

Reuben Brooks

University of Virginia ( email )

1400 University Ave
Charlottesville, VA 22903
United States

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