OneFactorStudentCopula Class Reference

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

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

Inheritance diagram for OneFactorStudentCopula:

List of all members.

Public Member Functions

 OneFactorStudentCopula (const Handle< Quote > &correlation, int nz, 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 Double Student t-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 $) and $ M $ ($ D_M $) to Student t-distributions with $ N_z $ and $ N_m $ degrees of freedom, respectively.

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, variables $ Z $ and $ M $ are scaled by $ \sqrt{(N_z - 2) / N_z} $ and $ \sqrt{(N_m - 2) / N_m}, $ respectively.

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.