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FRM Part II · FRM Exam Part II · Non-parametric Approaches

A risk analyst at a bank has 500 daily P&L observations and wants a confidence interval around the 99% historical simulation VaR estimate. She resamples the 500 observations with replacement many times, computes VaR on each resampled set, and uses the distribution of those VaRs. Which description best identifies this procedure and its main purpose?

This is bootstrap historical simulation. Drawing samples with replacement from the observed P&L and recomputing VaR each time produces a distribution of VaR estimates, which shows how precise the original estimate is and allows a confidence interval to be built.

  1. ABootstrap historical simulation, used to assess the precision of the VaR estimateCorrect
  2. BAge-weighted historical simulation, used to give recent data more influence
  3. CVolatility-weighted historical simulation, used to adjust for changing volatility
  4. DFiltered historical simulation, used to impose a GARCH structure on the returns

Explanation

Resampling the original data with replacement and recomputing VaR many times is the bootstrap. The spread of the resulting VaR estimates gives a measure of estimation precision, such as a confidence interval. The weighting approaches change observation weights rather than resample.

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