  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.
