OneFactorGaussianCopula

The one-factor Gaussian copula: each name's latent variable is X_i = sqrt(rho) M + sqrt(1 - rho) Z_i with a common systemic factor M and idiosyncratic Z_i, all standard normal. Name i defaults by t when X_i < Phi^{-1}(PD_i(t)).

Conditional on M, defaults are independent with probability p_i(M) = Phi( (Phi^{-1}(PD_i) - sqrt(rho) M) / sqrt(1 - rho) ) — the fact the PortfolioLossDistribution recursion and the large-homogeneous-pool (Vasicek) limit both rest on.

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Methods

static double conditionalDefaultProbability(double unconditionalPd, double rho, double m)

Default probability of a name conditional on the systemic factor m.

static double vasicekLossCdf(double x, double pd, double rho, double lgd)

The Vasicek large-homogeneous-pool loss distribution: the probability that the fractional portfolio loss is at most x, for unconditional default probability pd, correlation rho and loss given default lgd.

static double vasicekExpectedLoss(double pd, double lgd)

Expected fractional portfolio loss in the Vasicek limit (= pd * lgd).