Written in 1987; printed in *Derivatives Pricing: The Classic Collection*, P. Carr (ed.), London: Risk Books, 2004.

Consider a portfolio consisting of *n* loans in equal dollar amounts. Let the probability of default on any one loan be *p*, and assume that the values of the borrowing companies' assets are correlated with a coefficient ρ for any two companies. We wish to calculate the probability distribution of the percentage gross loss *L* on the portfolio, that is,

Let be the value of the *i*-th company's assets, described by a logarithmic Wiener process

where are Wiener processes with

The company defaults on its loan if the value of its assets drops below the contractual value of its obligations *D _{i}* payable at time

where

and ...

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