Using the Extremal Index for Value-at-Risk Backtesting*

Axel Bücher, Peter N Posch and Philipp Schmidtke

Journal of Financial Econometrics, vol. 18, issue 3, 556-584

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. For this purpose, we introduce a sequence of relative excess returns whose extremal index is 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.

Keywords: VaR backtesting; extremal index; independence; risk measures (search for similar items in EconPapers)
JEL-codes: C52 C53 C58 (search for similar items in EconPapers)
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