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Using the extremal index for value-at-risk backtesting

Authors
  • Bücher, Axel
  • Posch, Peter N.
  • Schmidtke, Philipp
Publication Date
Jan 01, 2018
Identifiers
DOI: 10.17877/DE290R-19196
OAI: oai:eldorado.tu-dortmund.de:2003/37201
Source
Eldorado - Ressourcen aus und für Lehre, Studium und Forschung
Keywords
Language
English
License
Unknown

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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