Loan portfolio value

Using a conditional independence framework, Oldrich Vasicek derives a useful limiting form for the portfolio loss distribution with a single systematic factor. He then derives a risk-neutral distribution suitable for traded portfolios, and shows how credit migration and granularity can be incorporated into this model too. This article was first published in the December 2002 issue of Risk

The amount of capital needed to support a portfolio of debt securities depends on the probability distribution of the portfolio loss. Consider a portfolio of loans, each of which is subject to default resulting in a loss to the lender. Suppose the portfolio is financed partly by equity capital and partly by borrowed funds. The credit quality of the lender's notes will depend on the probability that the loss on the portfolio exceeds the equity capital. To achieve a certain credit rating of its