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To calculate a percentile level, we must first specify the full distribution of portfolio values. For portfolios consisting of more than two exposures, this requires a simulation approach, which may be time-consuming. Our approach will be to generate possible portfolio scenarios at random according to a Monte Carlo framework. While the generation of scenarios may be time consuming, once we obtain these scenarios, the calculation of the 1st percentile level is simple. To do this, we first sort the portfolio values in ascending order.
As we have mentioned before, percentile levels are more meaningful statistics for large portfolios, where the portfolio can take on many different portfolio values. It is also the CreditMetrics™—Technical Document Sec. 5 Choosing a time horizon 31 case that for these large portfolios (in fact, for any portfolio with much more than two assets), it is necessary to perform simulations to compute percentile levels. Nonetheless, in order to provide an example, we compute percentile levels for our single bond.
00 There are at least four interesting features in the joint likelihood table above: 1. The probabilities across the table necessarily sum to 100%. 2. The most likely outcome is that both obligors simply remain at their current credit ratings. In fact, the likelihoods of joint migration become rapidly smaller as the migration distance grows. 3. The effect of correlation is generally to increase the joint probabilities along the diagonal drawn through their current joint standing (in this case, through BBB-A).