Asymptotic Distribution of the Sample Average Value-at-Risk in the Case of Heavy-Tailed Returns

Journal of Applied Functional Analysis, Vol. 3, pp. 443-461, 2008

18 Pages Posted: 24 Dec 2010

Date Written: November 6, 2007

Abstract

In this paper, we provide a stable limit theorem for the asymptotic distribution of the sample average value-at-risk when the distribution of the underlying random variable X describing portfolio returns is heavy-tailed. We illustrate the convergence rate in the limit theorem assuming that X has a stable Paretian distribution and Student's t distribution.

Keywords: average value-at-risk, risk measures, heavy-tails, asymptotic distribution, Monte Carlo method

JEL Classification: G32, C16

Suggested Citation

Stoyanov, Stoyan Veselinov and Rachev, Svetlozar, Asymptotic Distribution of the Sample Average Value-at-Risk in the Case of Heavy-Tailed Returns (November 6, 2007). Journal of Applied Functional Analysis, Vol. 3, pp. 443-461, 2008, Available at SSRN: https://ssrn.com/abstract=1730210

Stoyan Veselinov Stoyanov (Contact Author)

Charles Schwab ( email )

101 Montgomery Street (120K-15)
San Francisco, CA 94104
United States

Svetlozar Rachev

Texas Tech University ( email )

Dept of Mathematics and Statistics
Lubbock, TX 79409
United States
631-662-6516 (Phone)

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