The Uncertain Shape of Grey Swans: Extreme Value Theory with Uncertain Threshold

TL;DR

This paper introduces Uncertain EVT, a novel method that models the EVT threshold as a dynamic hidden variable to improve risk prediction accuracy in financial crises.

Contribution

It proposes a new framework where the EVT threshold is modeled as a state-dependent hidden variable, enhancing the forecasting of extreme financial risks.

Findings

Uncertain EVT outperforms traditional EVT in predicting large financial losses.

The model is competitive with established VaR models in back-testing.

Incorporating the BRT improves the capture of risk beyond the EVT threshold.

Abstract

Extreme Value Theory (EVT) is one of the most commonly used approaches in finance for measuring the downside risk of investment portfolios, especially during financial crises. In this paper, we propose a novel approach based on EVT called Uncertain EVT to improve its forecast accuracy and capture the statistical characteristics of risk beyond the EVT threshold. In our framework, the extreme risk threshold, which is commonly assumed a constant, is a dynamic random variable. More precisely, we model and calibrate the EVT threshold by a state-dependent hidden variable, called Break-Even Risk Threshold (BRT), as a function of both risk and ambiguity. We will show that when EVT approach is combined with the unobservable BRT process, the Uncertain EVT's predicted VaR can foresee the risk of large financial losses, outperforms the original EVT approach out-of-sample, and is competitive to well-known VaR models when back-tested for validity and predictability.