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I was wondering what the correct procedure is to follow when a VaR model fails a backtest (either conditional coverage and/or independence tests)?

Assuming I am restricted to using a historical VaR model, it seems that the only parameter than can be tuned is the lookback period of returns.

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Pages 8-11 of the BIS 1996 paper on backtesting provide very useful general guidance:

https://www.bis.org/publ/bcbs22.pdf

Hope this helps.

Many of these (positions mismatch, risk factors not captured, parameters not updated or calculated incorrectly) are as applicable to historical VaR as to any other VaR calculation approach.

In terms of the solution, in addition to the length of the observation period that you mentioned, one can also look at volatility scaling, improving the accuracy of the valuation, brining in additional risk factors etc. Understanding the causes is therefore very important when devising an improvement plan.

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Obviously, you biggest issue is the volatility. If you are restricted to use only Historical Simulation VaR, then consider incorporating conditional volatility to the model. Your backtesting will definitely improve if you do this.

Resources:

  1. An overview of Filtered Historical Simulation (FHS)
  2. Using Bootstrapping and Filtered Historical Simulation to Evaluate Market Risk
  3. Filtered historical simulation Value-at-Risk models and their competitors
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