Exposure at Default - Simulating Default Time

Overview

Simulating Default Times

The usual assumption for simulating a default time is that the distribution of times is uniform over the default interval. This can be done simply as

which calculates the fraction of the period at which default occurs.

For simulations that assume that the probability of default changes over time, the modeler can try either try to find a distribution which matches their assumptions, or break up the default interval into smaller intervals for which the default time can be reasonably be assumed to be nearly uniform.

Simulating Principal

To get the principal, the default time needs to be converted to a time which represents the number periods (and therefore the number of payments) that have elapsed for the loan in question.

For example, once the number of periods is known, the remaining principal can be calculated, as is done with an amortized loan

For more general forecasting of payments and principal, please see Forecasting Cashflows and Accruals