OneFactorStudentGaussianCopula Class Reference

One-factor Student t - Gaussian Copula. More...

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

Inheritance diagram for OneFactorStudentGaussianCopula:

List of all members.

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

\[ Y_i = a_i\,M+\sqrt{1-a_i^2}\:Z_i \]

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 $ \nu $ degrees of freedom is $ \nu / (\nu - 2) $. Since the copula approach requires zero mean and unit variance distributions, $ M $ is scaled by $ \sqrt{(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.