# OneFactorStudentGaussianCopula (3) - Linux Man Pages

## NAME

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.

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

Implements OneFactorCopula.

## Author

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