Vasicek Variance Test

PD

Numerical Integration Result

Monte Carlo Simulation: Enter # Trials

The **Vasicek distribution** describes the probability density
function for the fraction of defaulted loans within
an infinitely diversified portfolio. Simple but restrictive
assumptions specify a single default probability (PD) common
to each loan and a single correlation parameter linking the
behavior of all loans.

**Variance Test:** The numerical integration and Monte
Carlo simulation are two viable methods to compute the
variance of this Vasicek distribution - very important for
understanding the risk of the loan portfolio!

**Pool Test:**
Create an arbitrary number of pools with an arbitrary number of obligors per pool.
Apply Monte Carlo simulation to determine fraction of defaults in each pool.
Then compare to the analytical Vasicek distribution.

Vasicek Pool Test

Enter # Pools