Implements the Cornish-Fisher expansion for arbitrary orders. The algorithm is related, but not identical to, the algorithm "AS269" published in "Applied Statistics".
computes the Fourier transform of an approximating Gaussian cumulative distribution function (CDF) for the class of quadratic forms of Gaussian vectors.
Simulates a default distribution for a portfolio of homogeneous obligors where the default driver is normally distributed. Returns mean, variance and the quantile chosen.
Simulates a default distribution for a portfolio of obligors where the (joint) default driver is normally distributed. The dependence structure imposed corresponds to two homogeneous subportfolios driven by two default factors. Returns mean, variance and the quantile chosen.
Simulates a default distribution for a portfolio of homogeneous obligors where individual default drivers are normally distributed. The joint distribution is generated by the use of a t-copula. Returns mean, variance and the quantile chosen.
Simulates a default distribution for a portfolio of obligors where the individual default driver is normally distributed. The dependence structure imposed corresponds to two homogeneous subportfolios driven by two default factors linked by a t-copula. Returns mean, variance and quantile chosen.
uses a generalized eigenvalue decomposition to do a suitable coordinate change. The new risk factors are independently standard normal distributed and the new Hessian matrix (Gamma) is diagonal.
computes the a-quantile for the class of quadratic forms of Gaussian vectors; uses Fourier inversion to approximate the cumulative distribution function (CDF).