OneFactorStudentGaussianCopula (3) - Linux Manuals
OneFactorStudentGaussianCopula: One-factor Student t - Gaussian Copula.
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.
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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