On the Elliptic Distribution and Its Application to Leptokurtic Financial Data

57 Pages Posted: 3 Dec 2015

See all articles by Stephen H.T. Lihn

Stephen H.T. Lihn

Novus Partners, Inc.; Atom Investors LP

Date Written: September 26, 2015

Abstract

A novel distribution based on elliptic curves is developed to capture major leptokurtic features in the return distribution of financial assets. This distribution is based on the Weierstrass equation and depressed cubic polynomial; therefore, it is intuitive, mathematically elegant, analytically tractable, and easy to calculate. It fits well to the historical daily log-return distributions of currencies, commodities, Treasury yields, VIX, and, most difficult of all, DJIA whose kurtosis is above 20. Various asymptotic behaviors are studied that encompasses a wide range of kurtosis from 2.3 to 35. The formal expansion near O of elliptic curves also suggests a possible different perspective on the tail behavior of the financial data. The numerical methods are built into an R package. A comprehensive sqlite database stores pre-calculated statistical attributes that cover a large parameter space. This allows practitioners to quickly examine any time series of interest. The distribution serves as a viable alternative to other fat-tailed distributions used in financial and risk modeling.

Keywords: distribution, elliptic curves, timeseries, fat tail, leptokurtic, financial data, daily log-return

JEL Classification: C10, C63

Suggested Citation

Lihn, Stephen H.T. and Lihn, Stephen H.T., On the Elliptic Distribution and Its Application to Leptokurtic Financial Data (September 26, 2015). Available at SSRN: https://ssrn.com/abstract=2697911 or http://dx.doi.org/10.2139/ssrn.2697911

Stephen H.T. Lihn (Contact Author)

Atom Investors LP ( email )

3711 S Mopac Expressway
Austin, TX 78746
United States
917-603-4133 (Phone)

Novus Partners, Inc. ( email )

521 5th Ave
29th Floor
New York, NY 10175
United States
917-603-4133 (Phone)

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