Conditional Value-at-Risk for Uncommon Distributions

Abstract

Conditional Value-at-Risk (CVaR) represents a significant improvement over the Value-at-Risk (VaR) in the area of risk measurement, as it catches the risk beyond the VaR threshold. CVaR is also theoretically more solid, being a coherent risk measure, which enables building more robust risk assessment and management systems. This paper addresses the derivation of the closed-form CVaR formulas for several less known distributions, such as Burr type XII, Dagum, hyperbolic secant, as well as more popular generic extreme value distributions. It follows an unnoticed result of Patrizia Stucchi who derived CVaR formulas for Johnson’s SU/SB/SL distributions. While being uncommon for general public, those distributions represent a significant advancement in modeling financial assets returns. After having derived the closed-form CVaR formulas for the most popular elliptic distributions and log-distribution, this paper concludes the development of mathematical toolbox required for effective introduction of CVaR into practical risk management.

Keywords: CVaR, Conditional Value at Risk, Risk Management, Burr Distribution, Dagum Distribution, Generic Extreme Value Distribution, Hyperbolic Secant Distribution

JEL Classification: G32, C46