Conditional value-at-risk estimation using non-integer values of degrees of freedom in Student's t-distribution

Andriy Andreev, Antti Kanto

Abstract

ABSTRACT

This paper provides an analytical formula for CVAR calculated using t-distributions with non-integer degrees of freedom. We generalize standard formulas, calculated on the assumption of normal log-returns without compromising on the difficulty of the calculation procedure involved. We also extend the results of Heikkinen and Kanto (2002) to show the impact of kurtosis on values of CVAR. The results are summarized in a closed-form formula that can, with little effort, be used by risk managers in the evaluation risk exposures for a family of heavy-tailed distributions.