Computing VAR and AVaR in Infinitely Divisible Distributions
37 Pages Posted: 8 May 2009
Date Written: March 2009
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: Suggested Citation