OneFactorStudentGaussianCopula (3) Linux Manual Page

QuantLib::OneFactorStudentGaussianCopula – One-factor Student t – Gaussian Copula.

Synopsis

#include <ql/experimental/credit/onefactorstudentcopula.hpp>

Inherits QuantLib::OneFactorCopula.

Public Member Functions

OneFactorStudentGaussianCopula (const Handle< Quote > &correlation, int nm, Real maximum=10, Size integrationSteps=200)

Real density (Real m) const
Density function of M.
Real cumulativeZ (Real z) const
Cumulative distribution of Z.

Detailed Description

One-factor Student t – Gaussian Copula.

The copula model [ Y_i = a_i,M+qrt{1-a_i^2}:Z_i ] is specified here by setting the probability density functions for $ Z_i $ ($ D_Z $) to a Gaussian and for $ M $ ($ D_M $) to a Student t-distribution with $ N_m $ degrees of freedom.

The variance of the Student t-distribution with $ $ degrees of freedom is $ / ( – 2) $. Since the copula approach requires zero mean and unit variance distributions, $ M $ is scaled by $ qrt{(N_m – 2) / N_m}. $

Possible enhancements

Improve performance/accuracy of the calculation of inverse cumulative Y. Tabulate and store it for selected correlations?

Member Function Documentation

Real density (Real m) const [virtual]

Density function of M.

Derived classes must override this method and ensure zero mean and unit variance.

Implements OneFactorCopula.

Real cumulativeZ (Real z) const [virtual]

Cumulative distribution of Z.