Measuring Model Risk

TL;DR

This paper introduces a method to quantify model risk by assessing the sensitivity of expected loss to variations in the risk factor distribution, using divergence measures to identify worst-case scenarios.

Contribution

It provides formulas for calculating distribution model risk and worst-case distributions, incorporating divergence measures like relative entropy and f-divergences.

Findings

Formulas for distribution model risk calculation

Explicit determination of worst-case distributions

Application to ambiguity-averse decision making

Abstract

We propose to interpret distribution model risk as sensitivity of expected loss to changes in the risk factor distribution, and to measure the distribution model risk of a portfolio by the maximum expected loss over a set of plausible distributions defined in terms of some divergence from an estimated distribution. The divergence may be relative entropy, a Bregman distance, or an $f$-divergence. We give formulas for the calculation of distribution model risk and explicitly determine the worst case distribution from the set of plausible distributions. We also give formulas for the evaluation of divergence preferences describing ambiguity averse decision makers.