Probabilistic model for risk factors

The basic dichotomy here is between parametric and non-parametric models. In
parametric models, the probability distribution of the risk factors is assumed to be
of a specific functional form, e.g. jointly normal, with parameters estimated from
historical time series. In non-parametric models, the probability distribution of changes in the risk factors is taken to be precisely the distribution that was observed
empirically over some interval of time in the past. The non-parametric approach is
what is generally known as historical VaR.
Parametric models have the following advantages:
1 The relevant information from historical time series is encapsulated in a relatively
small number of parameters, facilitating its storage and transmission.
2 Since the distribution of the market data is assumed to be of a specific functional
form, it may be possible to derive an analytic form for the distribution of the value
of the portfolio. An analytic solution can significantly reduce computation time.
3 It is possible to get good estimates of the parameters even if the individual time
series have gaps, due to holidays, technical problems, etc.
4 In the case of RiskMetrics, the necessary data is available for free.
Parametric models have the following disadvantages:
1 Real market data is, at best, imperfectly described by the commonly used approximating
distributions. For example, empirical distributions of log returns have
skewed fat tails and it is intuitively implausible to model volatilities as being
jointly normal with their underlyings.
2 Since one does not have to worry about model assumptions, non-parametric
models are more flexible, i.e. it is easy to add new variables.
3 In the opinion of some, non-parametric models are more intuitive.