A Generalized Asymmetric Student-t Distribution with Application to Financial Econometrics

39 Pages Posted: 5 Nov 2009

See all articles by John W. Galbraith

John W. Galbraith

McGill University - Department of Economics; Center for Interuniversity Research and Analysis on Organization (CIRANO)

Dongming Zhu

Peking University

Date Written: April 1, 2009

Abstract

This paper proposes a new class of asymmetric Student-t (AST) distributions, and investigates its properties, gives procedures for estimation, and indicates applications in financial econometrics. We derive analytical expressions for the cdf, quantile function, moments, and quantities useful in financial econometric applications such as the expected shortfall. A stochastic representation of the distribution is also given. Although the AST density does not satisfy the usual regularity conditions for maximum likelihood estimation, we establish consistency, asymptotic normality and efficiency of ML estimators and derive an explicit analytical expression for the asymptotic covariance matrix. A Monte Carlo study indicates generally good finite-sample conformity with these asymptotic properties.

Keywords: asymmetric distribution, expected shortfall, maximum likelihood estimation

JEL Classification: C13, C16

Suggested Citation

Galbraith, John W. and Zhu, Dongming, A Generalized Asymmetric Student-t Distribution with Application to Financial Econometrics (April 1, 2009). Available at SSRN: https://ssrn.com/abstract=1499914 or http://dx.doi.org/10.2139/ssrn.1499914

John W. Galbraith (Contact Author)

McGill University - Department of Economics ( email )

1001 Sherbrooke St. W
Montreal, Quebec H3A 1G5
Canada

Center for Interuniversity Research and Analysis on Organization (CIRANO) ( email )

2020 rue University, 25th floor
Montreal H3C 3J7, Quebec
Canada

Dongming Zhu

Peking University ( email )

No. 38 Xueyuan Road
Haidian District
Beijing, Beijing 100871
China

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