Reverse Sensitivity Analysis for Risk Modelling

TL;DR

This paper introduces a model-free reverse sensitivity analysis method that determines how to stress the output distribution of a risk model in Wasserstein distance, and efficiently computes the corresponding stressed input distribution using Monte Carlo samples.

Contribution

It develops a novel reverse sensitivity analysis framework for risk models, deriving stressed distributions closest in Wasserstein distance, with an efficient computational approach and an R package implementation.

Findings

Provides a closed-form solution for stressed distributions under output constraints

Enables stress testing on mean, variance, risk measures, and utility functions

Implemented in R package SWIM for practical use

Abstract

We consider the problem where a modeller conducts sensitivity analysis of a model consisting of random input factors, a corresponding random output of interest, and a baseline probability measure. The modeller seeks to understand how the model (the distribution of the input factors as well as the output) changes under a stress on the output's distribution. Specifically, for a stress on the output random variable, we derive the unique stressed distribution of the output that is closest in the Wasserstein distance to the baseline output's distribution and satisfies the stress. We further derive the stressed model, including the stressed distribution of the inputs, which can be calculated in a numerically efficient way from a set of baseline Monte Carlo samples and which is implemented in the R package SWIM on CRAN. The proposed reverse sensitivity analysis framework is model-free and allows for stresses on the output such as (a) the mean and variance, (b) any distortion risk measure including the Value-at-Risk and Expected-Shortfall, and (c) expected utility type constraints, thus making the reverse sensitivity analysis framework suitable for risk models.