Credit Loss Calculator

The expected loss from the guarantor’s perspective is maximum lossprobability 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.

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

The key determinant in Monte Carlo simulation is the underlying stochastic process. Monte Carlo simulation can be used to generate a “random walk” based on the underlying stochastic process. When Monte Carlo approach is used, we first generate a series of random numbers based on the distribution of random term in the PDE. By combining this random effect and the main trend (drift) of the stochastic variable, a path is simulated. By repeating this process, we can produce more paths for underlying variable. However, a great amount of trials should be undertaken so as to generate an unbiased result.

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.

Credit Loss Calculator

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