Simulating Number of Payments

Overview

A quick an dirty approach to calculating EAD is the simulate the number of payments that have occurred up to default. That is, if n number of payments can occur during the period in question, you simulate a number from 0 to n, and take that as the number of payments that occurred in the period prior to default.

This means that you can mostly bypass having to deal with date and time logic, and get an answer that is close enough.

Example

The simulated bond makes 2 payments per year. The period being simulated is a year, so the modeler simulates either 0,1, or 2 payments. A simple rule of thumb would be that the period being simulated is guestimated to start exactly in the middle of the last payment and the next payment. That means there is 3 months where no payment is made, then a payment is made, then 6 months, and then the last payment. So the probability of 0 payments would be 0.25, the probability of 1 payment is 0.5, and the probability of 2 payments would be 0.25.