Measuring Solvency Risk Using Flexible Distributions: An Analysis for the Colombian Banking System

Abstract

This paper proposes using Gram-Charlier Type A probability distributions to measure solvency risk. The method assesses the likelihood of a bank’s solvency falling below the minimum ratio set by regulators. Applied to 15 banks in Colombia, the study reveals the importance of considering the proximity of the Capital Adequacy Ratio (CAR) to the regulatory minimum and the probability distribution of solvency changes. Gram-Charlier Type A functions offer a better fit than the normal distribution. These findings hold significance for regulators and decision-makers, emphasizing the need to incorporate suitable measures for assessing solvency risk in banks.

Keywords:

• Gram-Charlier expansions
• quantile risk metrics
• semi-nonparametric approach
• solvency risk

JEL CLASSIFICATION CODES:

• C14
• C22
• C54
• G21
• G28

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Data is available upon request.

Code availability statement

The R code for performing estimations is available upon request.

Notes

1 Straightforward computations yield the following expressions for the first eight Hermite polynomials: $H_0\left(z\right)=1,{ H}_1\left(z\right)=z,$ $H_2\left(z\right)=z^2-1,H_3\left(z\right)=z^3-3z,H_4\left(z\right)=z^4-6z^2+3,H_5\left(z\right)=z^5-10z^3+15z,$ $H_6\left(z\right)=z^6-15z^4+45z^2-15,{ H}_7\left(z\right)=z^7-21z^5+105z^3-105z,H_8\left(z\right)=z^8-28z^6+210z^4-420z^2+105.$

Additional information

Funding

This study was funded by Instituto Tecnologico Metropolitano (ITM) and Universidad EAFIT [project 952-000050].