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