Risk Measures and Credit Risk Under the Beta-Kotz Distribution

TL;DR

This paper introduces a new method for estimating risk measures like VaR and CVaR under the Beta-Kotz distribution, enhancing credit risk assessment with analytical and numerical techniques.

Contribution

It develops a novel approach for calculating risk measures assuming Beta-Kotz distributed risk factors, including parameter estimation and application to credit risk.

Findings

Analytical formulas for risk measures in special cases.

Numerical methods for general Beta-Kotz parameters.

Application to credit risk quantification.

Abstract

This paper considers the use for Value-at-Risk computations of the so-called Beta-Kotz distribution based on a general family of distributions including the classical Gaussian model. Actually, this work develops a new method for estimating the Value-at-Risk, the Conditional Value-at-Risk and the Economic Capital when the underlying risk factors follow a Beta-Kotz distribution. After estimating the parameters of the distribution of the loss random variable, both analytical for some particular values of the parameters and numerical approaches are provided for computing these mentioned measures. The proposed risk measures are finally applied for quantifying the potential risk of economic losses in Credit Risk.