PortfolioLossDistribution

The portfolio loss distribution under the one-factor Gaussian copula, by the Andersen-Sidenius-Basu recursion: conditional on the systemic factor the per-name default indicators are independent, so the number of defaults is a Poisson-binomial whose distribution is built by convolving one name in at a time; the unconditional distribution is a Gauss-Hermite integral over the factor.

This build assumes a homogeneous loss given default so losses fall on an integer grid of "one defaulted name". Heterogeneous notionals or recoveries are a bucketed extension of the same recursion.

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Methods

static PortfolioLossDistribution homogeneous(double pd, int names, double rho, double lgd, int nodes)

pd: unconditional default probability per name to the horizon (same for every name)
names: pool size
rho: copula correlation
lgd: loss given default, as a fraction of one name's notional
nodes: Gauss-Hermite nodes for the factor integral (e.g. 64)

double probabilityOfDefaults(int k)

P(k names defaulted).

double expectedLoss()

Expected fractional portfolio loss.

double expectedTrancheLoss(double attach, double detach)

Expected loss of the tranche [attach, detach] (as fractions of the portfolio), i.e. E[ min(max(L - attach, 0), detach - attach) ].