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QuantLib_OneFactorStudentCopula

NAME

QuantLib::OneFactorStudentCopula -

One-factor Double Student t-Copula.

SYNOPSIS

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

Inherits QuantLib::OneFactorCopula.

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+qrt{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 $ $ degrees of freedom is $ / ( - 2) $. Since the copula approach requires zero mean and unit variance distributions, variables $ Z $ and $ M $ are scaled by $ qrt{(N_z - 2) / N_z} $ and $ qrt{(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.

Author

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