Risk calculation engine

The last component is the risk calculation engine which actually calculates the
expected returns and multivariate distributions that are then used to calculate the
associated risks and the optimal portfolio. Since the distributions are not normal,
this portion of the portfolio model requires some ingenuity.
One method of calculation is Monte Carlo simulation. This is exemplified in
many of the above-mentioned models. Another method of calculating the probability
distribution is numerical. One starts by approximating the probability distribution
of losses for each asset by a discrete probability distribution. This is a reasonable
simplification because one is mainly interested in large, collective losses – not
individual firm losses.
Once the individual probability distributions have been discretized, there is a
well-known computation called convolution for computing the aggregate probability
distribution. This numerical method is easiest when the probability distributions are
independent – which in this case they are not. There are tricks and enhancements
to the convolution technique to make it work for nonindependent distributions.
The risk calculation engine of CreditRiskò uses the convolution. It models the
nonindependence of defaults with a factor model. It assumes that there is a finite
number of factors which describe nonindependence. Such factors would come from
the firm’s country, geographical location, industry, and specific characteristics.