Quantile-Based Inference for Tempered Stable Distributions

25 Pages Posted: 20 Jun 2015 Last revised: 12 Jul 2016

See all articles by Hasan Fallahgoul

Hasan Fallahgoul

Monash University

David Veredas

Vlerick Business School

Frank J. Fabozzi

EDHEC Business School

Date Written: June 19, 2015

Abstract

If the closed-form formula for the probability density function is not available, implementing the maximum likelihood estimation is challenging. We introduce a simple, fast, and accurate way for the estimation of numerous distributions that belong to the class of tempered stable probability distributions. Estimation is based on the Method of Simulated Quantiles (Dominicy and Veredas (2013)). MSQ consists of matching empirical and theoretical functions of quantiles that are informative about the parameters of interest. In the Monte Carlo study we show that MSQ is significantly faster than Maximum Likelihood and the estimates are almost as precise as MLE. A Value at Risk study using 13 years of daily returns from 21 world-wide market indexes shows that MSQ estimates provide as good risk assessments as with MLE.

Keywords: heavy tailed distribution, tempered stable distribution, method of simulated quantiles

JEL Classification: C5, G12

Suggested Citation

Fallahgoul, Hasan A and Veredas, David and Fabozzi, Frank J., Quantile-Based Inference for Tempered Stable Distributions (June 19, 2015). Available at SSRN: https://ssrn.com/abstract=2620621 or http://dx.doi.org/10.2139/ssrn.2620621

Hasan A Fallahgoul

Monash University ( email )

Clayton Campus
Victoria, 3800
Australia

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

David Veredas (Contact Author)

Vlerick Business School ( email )

Library
REEP 1
Gent, BE-9000
Belgium

Frank J. Fabozzi

EDHEC Business School ( email )

France
215 598-8924 (Phone)

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