Computing the distribution of the portfolio value

If the risk factors are modeled non-parametrically, i.e. for historical VaR, the time
series of changes in the risk factors are applied one by one to the current values of
the risk factors and the portfolio revalued under each scenario. The distribution of
portfolio values is given simply by the resulting histogram. A similar approach can
be used for parametric models, replacing the historical perturbations by pseudorandom
ones drawn from the parametric model. This is termed Monte Carlo VaR.
Alternatively, if one makes certain simplifying assumptions, one can compute the
distribution of portfolio values analytically. For example, this is done in the Risk-
Metrics methodology. The benefit of analytic methodologies is that their computational
burden is much lower. In addition, analytic methods may be extended to give
additional insight into the risk profile of a portfolio.