On a Poisson Subordinated Distribution for Precise Statistical Measurement of Leptokurtic Financial Data

Abstract

A new Poisson subordinated distribution is proposed to capture major leptokurtic features in log-return time series of financial data. This distribution is intuitive, easy to calculate, and converge quickly. Analytic formula exists for all moments for the entire parameter space. It fits well to the historical daily log-return distributions of currencies, commodities, Treasury yields, VIX, and, most difficult of all, DJIA. It serves as a viable alternative to the Student’s t-distribution and the more sophisticated truncated stable distribution.

Keywords: Subordination, Poisson distribution, financial data, fat tail, leptokurtotic, Student's t-distribution, Stable distribution, daily log-return, finite moment

JEL Classification: C61, C63