Conditional Value at Risk and Partial Moments for the Metalog Distributions

TL;DR

This paper advances the metalog distributions by deriving closed-form expressions for Conditional Value at Risk and partial moments, enhancing their application in risk management with explicit formulas and convexity properties.

Contribution

It provides the first closed-form expressions for CVaR and partial moments for metalog distributions, improving their utility in risk analysis.

Findings

Closed-form CVaR expressions derived for metalog distributions

Partial moments are shown to be convex functions of parameters

Enhances practical application of metalog distributions in risk management

Abstract

The metalog distributions represent a convenient way to approach many practical applications. Their distinctive feature is simple closed-form expressions for quantile functions. This paper contributes to further development of the metalog distributions by deriving the closed-form expressions for the Conditional Value at Risk, a risk measure that is closely related to the tail conditional expectations. It also addressed the derivation of the first-order partial moments and shows that they are convex with respect to the vector of the metalog distribution parameters.