Historical simulation as a method for estimating VaR was introduced in a series of papers by Boudoukh et al. (1998) and Barone-Adesi et al. (1998, 1999). A recent survey suggests that about three-quarters of banks prefer to use historical simulation rather the parametric linear or Monte Carlo VaR methodologies.^{1} Why should this be so – what are the advantages of historical simulation over the other two approaches?

The main advantage is that historical VaR does not have to make an assumption about the parametric form of the distribution of the risk factor returns. Although the other models can include skewed and heavy tailed risk factor returns, they must still fit a parametric form for modelling the multivariate risk factor returns. And usually the dependencies between risk factors in this multivariate distribution are assumed to be much simpler than they are in reality.

For instance, the parametric linear model assumes that risk factor return dependencies are linear and are fully captured by one or more correlation matrices. This is also commonly assumed in Monte Carlo VaR, although here it is possible to assume more complex dependency structures as explained in the next chapter. Also, the parametric linear VaR model is a *one*-*step* model, based on the assumption that risk factor returns are i.i.d. There is no simple way that path-dependent behaviour such as *volatility clustering* can be accounted for in this framework. Monte Carlo VaR ...

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