Overview
Parametric models are models where the porfolio distribution is assumed to be of a given mathematical form, with only a set of parameters needed to specify it completely. The canonical example is the assumption that the portfio value is normally distributed.
Normal Assumption
A simple portfolio distribution assumption is that portfolio returns, or portfolio log returns are normally distributed. Then the portfolio VAR can be calculated as
{% VAR = \Phi ^{-1}(1 - \alpha)\sigma - \mu %}
where {% \Phi %} is the normal
cumulative function.
The normal distribution parameters that represent the portfolio returns are estimated using the standard portfolio standard deviation tools.