Using the extremal index for value-at-risk backtesting

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Date

2018

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Abstract

We introduce a set of new Value-at-Risk independence backtests by establishing a connection between the independence property of Value-at-Risk forecasts and the extremal index, a general measure of extremal clustering of stationary sequences. We introduce a sequence of relative excess returns whose extremal index has to be estimated. We compare our backtest to both popular and recent competitors using Monte-Carlo simulations and find considerable power in many scenarios. In an applied section we perform realistic out-of-sample forecasts with common forecasting models and discuss advantages and pitfalls of our approach.

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Keywords

VaR backtesting, risk measures, independence, extremal index

Subjects based on RSWK

Value at Risk, Statistischer Test, Schätzverfahren, Extremwertstatistik

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