Estimating VaR in credit risk: Aggregate vs single loss distribution

TL;DR

This paper compares aggregate and single loss distribution methods for estimating VaR in credit risk, introducing a new technique for high-confidence quantile calculation and analyzing the impact of severity distribution choices.

Contribution

It presents a novel approach for calculating high-confidence quantiles of the Gamma distribution and compares aggregate versus single loss VaR estimates using different severity models.

Findings

Truncated exponential severity distribution yields VaR estimates closer to aggregate models.

Deviations between models depend on portfolio size and loss truncation.

New method improves quantile estimation for Gamma distributions at high confidence levels.

Abstract

Using Monte Carlo simulation to calculate the Value at Risk (VaR) as a possible risk measure requires adequate techniques. One of these techniques is the application of a compound distribution for the aggregates in a portfolio. In this paper, we consider the aggregated loss of Gamma distributed severities and estimate the VaR by introducing a new approach to calculate the quantile function of the Gamma distribution at high confidence levels. We then compare the VaR obtained from the aggregation process with the VaR obtained from a single loss distribution where the severities are drawn first from an exponential and then from a truncated exponential distribution. We observe that the truncated exponential distribution as a model for the severities yields results closer to those obtained from the aggregation process. The deviations depend strongly on the number of obligors in the portfolio, but also on the amount of gross loss which truncates the exponential distribution.