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Credit Risk Calculation The expected loss from the guarantor’s perspective is maximum lossprobability of default(1-recovery rate). The maximum loss is the difference between CMB value and MBS value. We use ratings transition to estimate the probability of default and assume that the recovery rate is zero. The two legs of the swap are as follows: a bond and a VRM (once reinvestment is considered, the amortizing nature of the VRM disappears). Thus the swap is like a conventional “receive fixed pay floating” swap. As the duration (sensitivity) is essentially one month, the price of VRM-MBS will always be close to par. It follows that the worst-case scenario will happen in a downward interest rates environment where the CMB price goes up and exceeds the MBS value. However, the CMB price will get back to par as the maturity approaches. Consequently, the worst-case scenario is likely to occur sometime in the middle of the term. As described in the Credit Risk Calculator documentation, we can assume that the forward rates follow a lognormal process as follows: The figure below is a Monte Carlo simulation of short-term rates (not the forward rates in our case --we will explain the relationships later). As illustrated in the diagram, if we use a 95% confidence interval to build upper and lower boundaries according to the underlying stochastic process, we have 95% chance for the rates simulated to fall within these limits. As you can see in the diagram, Monte Carlo simulation is basically reproducing the underlying distribution already defined by the underlying stochastic process. In the credit risk analysis, we don’t care what is happening in the middle of the interval when using Monte Carlo simulation. What matters to us is the worst-case scenario, which is the lower bound. Consequently, we can calculate directly the lower bound and find out the worst-case scenario.
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