Vasicek Distribution
From Open Risk Manual
Definition
The Vasicek Distribution is a special probability distribution that emerges in the context of Threshold Models used in credit portfolio modelling. It was first introduced in[1]. There are two versions, the finite portfolio case and its limiting case wher the number of exposures in a portfolio assumed infinitely many / infinitely small.
Finite Portfolio Case
In the finite case the probability mass of D=k defaults out of a pool of N credits with equal probability of default p is
![{\displaystyle P[D=k]=\int _{0}^{\infty }{\binom {N}{k}}p^{k}(x)(1-p(x))^{N-k}G(dx)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/124e4c86f2b0eccdbce8acd9cacd6022b11d2b6f)
where G(z) denotes the inverse cumulative distribution function
Limit Case
The limit case arrises as a limit distribution of the sum of conditionally independent Bernulli variables
Usage
Used extensively in as a simple model of portfolio loss (also in Basel II as the ASRF model)
Seel Also
References
- ↑ Vasicek O., Probability of loss on loan portfolio, 1987
