One of the most popular ways of modeling defaults is the so-called asset-value approach. Using this approach we assume that if the value of a firm's assets falls below a certain level it will be beneficial for the owners to let the firm default: paying out the existing debt would leave them worse off.

Although this model provides for a very stylised representation of reality, it is a very convenient tool to simulate firms' defaults. The first step in doing so is to specify the default probability (PD). The next step is assuming that the asset value follows a geometric Brownian motion - its increments follow the standard normal distribution. Thus we generate independent standard normal variables for each time period and when the cumulative process hits the trigger we regard the exposure as a defaulted one. The trigger level is given by the inverse of the standard normal distribution evaluated at the probability of default.

By describing each firm's asset value by a common systematic risk factor and an idiosyncratic shock the model incorporates correlation across the assets.