Computing VAR and AVaR in Infinitely Divisible Distributions

37 Pages Posted: 8 May 2009

See all articles by Young Shin Kim

Young Shin Kim

University of Karlsruhe

Svetlozar Rachev

Texas Tech University

Michele Leonardo Bianchi

Bank of Italy

Frank J. Fabozzi

EDHEC Business School

Date Written: March 2009

Abstract

In this paper we derive closed-form solutions for the cumulative density function and the average value-at-risk for five subclasses of the infinitely divisible distributions: classical tempered stable distribution, Kim-Rachev distribution, modified tempered stable distribution, normal tempered stable distribution, and rapidly decreasing tempered stable distribution. We present empirical evidence using the daily performance of the S&P 500 for the period January 2, 1997 through December 29, 2006.

Keywords: tempered stable distribution, infinitely divisible distribution, value-at-risk, conditional value-at-risk, average value-at-risk

JEL Classification: G11, G21

Suggested Citation

Kim, Young Shin and Rachev, Svetlozar and Bianchi, Michele Leonardo and Fabozzi, Frank J., Computing VAR and AVaR in Infinitely Divisible Distributions (March 2009). Yale ICF Working Paper No. 09-07, Available at SSRN: https://ssrn.com/abstract=1400965 or http://dx.doi.org/10.2139/ssrn.1400965

Young Shin Kim

University of Karlsruhe ( email )

Postbox
76128 Karlsruhe, DE 76128
Germany

Svetlozar Rachev

Texas Tech University ( email )

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

Michele Leonardo Bianchi

Bank of Italy ( email )

Via Nazionale 91
00184 Rome, I - 00184
Italy

Frank J. Fabozzi (Contact Author)

EDHEC Business School ( email )

France
215 598-8924 (Phone)

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