Loss Distribution Model

This app illustrates one piece of a model used in the banking industry to forecast loan defaults. The model is called the Vasicek Single-Factor Model and the idea behind this piece of the model is to set a default threshold and see how many times the loan crosses the threshold after many random trials.

The model assumes that uncertainty on credit \(i\) is driven by a latent, unbserved factor, \(X_i\), with the following properties: \[X_i = \sqrt{\rho}*Z + \sqrt{1-\rho}*Zvar_i\] where

• \(Z\) is a common systemic risk factor affecting all firms (e.g., the state of the economy)

• \(Zvar_i\) is an idiosyncratic factor independent for each firm (e.g., management, innovations, sales, etc.)

• \(\rho\) is the correlation coefficient between each firm and is the same for any two firms

Credit \(i\) is assumed to default when its latent factor \(X_i\) takes on a value less than a credit-specific threshold,

\(X_i < Threshold\).

To illustrate how this would work for a single borrower, let's set the PD for our borrower at 8% and run the simulation using the latent factor \(X_i\) to determine how many times in M iterations we get a default. We'll notice that when M is small (in this example we only run the simulation 20 times), the default rate will likely not be 8%, but as M gets larger we will begin to approximate 8% (i.e., in the long run our default rate will converge on the expected rate).

## DefaultRate 
##        0.05

So, if we didn't get an 8% default rate last time, will we get it when we run the simulation more times? Yes, as we can see below we approximate an 8% default rate when M is large.

## DefaultRate 
##       0.079