Theoretical Sensitivity Analysis for Quantitative Operational Risk Management

TL;DR

This paper analyzes how the Value at Risk (VaR) changes when an additional loss factor is added to a heavy-tailed loss distribution, providing asymptotic results relevant for operational risk sensitivity analysis.

Contribution

It offers a theoretical framework for understanding the asymptotic behavior of VaR differences under heavy-tailed loss distributions in operational risk management.

Findings

VaR difference asymptotically equals expected loss of S when S's tail is thinner.

Different tail relationships lead to distinct asymptotic behaviors.

Results inform sensitivity analysis in Basel II/III frameworks.

Abstract

We study the asymptotic behavior of the difference between the values at risk VaR(L) and VaR(L+S) for heavy tailed random variables L and S for application in sensitivity analysis of quantitative operational risk management within the framework of the advanced measurement approach of Basel II (and III). Here L describes the loss amount of the present risk profile and S describes the loss amount caused by an additional loss factor. We obtain different types of results according to the relative magnitudes of the thicknesses of the tails of L and S. In particular, if the tail of S is sufficiently thinner than the tail of L, then the difference between prior and posterior risk amounts VaR(L+S) - VaR(L) is asymptotically equivalent to the expectation (expected loss) of S.