LO 2.1: Apply the bootstrap historical simulation approach to estimate coherent risk measures.
The bootstrap historical simulation is a simple and intuitive estimation procedure. In essence, the bootstrap technique draws a sample from the original data set, records the VaR from that particular sample and returns the data. This procedure is repeated over and over and records multiple sample VaRs. Since the data is always returned to the data set, this procedure is akin to sampling with replacement. The best VaR estimate from the full data set is the average of all sample VaRs.
This same procedure can be performed to estimate the expected shortfall (ES). Each drawn sample will calculate its own ES by slicing the tail region into n slices and averaging the VaRs at each of the n 1 quantiles. This is exactly the same procedure described in the previous topic. Similarly, the best estimate of the expected shortfall for the original data set is the average of all of the sample expected shortfalls.
Empirical analysis demonstrates that the bootstrapping technique consistently provides more precise estimates of coherent risk measures than historical simulation on raw data alone.
2018 Kaplan, Inc.
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Topic 2 Cross Reference to GARP Assigned Reading – Dowd, Chapter 4
U s i n g N o n -Pa r a m e t r i c E s t i m a t i o n
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