OneFactorCopula Class Reference
Abstract base class for one-factor copula models. More...
#include <ql/experimental/credit/onefactorcopula.hpp>

Public Member Functions | |
| OneFactorCopula (const Handle< Quote > &correlation, Real maximum=5.0, Size integrationSteps=50, Real minimum=-5.0) | |
| virtual Real | density (Real m) const =0 |
| Density function of M. | |
| virtual Real | cumulativeZ (Real z) const =0 |
| Cumulative distribution of Z. | |
| virtual Real | cumulativeY (Real y) const |
| Cumulative distribution of Y. | |
| virtual Real | inverseCumulativeY (Real p) const |
| Inverse cumulative distribution of Y. | |
| Real | correlation () const |
| Single correlation parameter. | |
| Real | conditionalProbability (Real prob, Real m) const |
| Conditional probability. | |
| std::vector< Real > | conditionalProbability (const std::vector< Real > &prob, Real m) const |
| Vector of conditional probabilities. | |
| Real | integral (Real p) const |
| template<class F > | |
| Real | integral (const F &f, std::vector< Real > &probabilities) const |
| template<class F > | |
| Distribution | integral (const F &f, const std::vector< Real > &nominals, const std::vector< Real > &probabilities) const |
| int | checkMoments (Real tolerance) const |
Protected Member Functions | |
| Size | steps () const |
| Real | dm (Size i) const |
| Real | m (Size i) const |
| Real | densitydm (Size i) const |
Protected Attributes | |
| Handle< Quote > | correlation_ |
| Real | max_ |
| Size | steps_ |
| Real | min_ |
| std::vector< Real > | y_ |
| std::vector< Real > | cumulativeY_ |
Detailed Description
Abstract base class for one-factor copula models.Reference: John Hull and Alan White, The Perfect Copula, June 2006
Let
be the cumulative probability of default of counterparty i before time t.
In a one-factor model, consider random variables
where
and
have independent zero-mean unit-variance distributions and
. The correlation between
and
is then
.
Let
be the cumulative distribution function of
.
is mapped to
such that percentiles match, i.e.
or
.
Now let
be the cumulated distribution function of
. For given realization of
, this determines the distribution of
:
The distribution functions of
are specified in derived classes. The distribution function of
is then given by the convolution
where
and
are the probability densities of
and
respectively.
This convolution can also be written
or
In general,
needs to be computed numerically.
- Possible enhancements:
- Improve on simple Euler integration
Member Function Documentation
| virtual Real density | ( | Real | m | ) | const [pure virtual] |
Density function of M.
Derived classes must override this method and ensure zero mean and unit variance.
Implemented in OneFactorGaussianCopula, OneFactorStudentCopula, OneFactorGaussianStudentCopula, and OneFactorStudentGaussianCopula.
| virtual Real cumulativeZ | ( | Real | z | ) | const [pure virtual] |
Cumulative distribution of Z.
Derived classes must override this method and ensure zero mean and unit variance.
Implemented in OneFactorGaussianCopula, OneFactorStudentCopula, OneFactorGaussianStudentCopula, and OneFactorStudentGaussianCopula.
| virtual Real cumulativeY | ( | Real | y | ) | const [virtual] |
Cumulative distribution of Y.
This is the default implementation based on tabulated data. The table needs to be filled by derived classes. If analytic calculation is feasible, this method can also be overridden.
Reimplemented in OneFactorGaussianCopula.
| virtual Real inverseCumulativeY | ( | Real | p | ) | const [virtual] |
Inverse cumulative distribution of Y.
This is the default implementation based on tabulated data. The table needs to be filled by derived classes. If analytic calculation is feasible, this method can also be overridden.
Reimplemented in OneFactorGaussianCopula.
| Real conditionalProbability | ( | Real | prob, | |
| Real | m | |||
| ) | const |
Conditional probability.
| std::vector<Real> conditionalProbability | ( | const std::vector< Real > & | prob, | |
| Real | m | |||
| ) | const |
Vector of conditional probabilities.
| Real integral | ( | Real | p | ) | const |
Integral over the density
of M and the conditional probability related to p:
| Real integral | ( | const F & | f, | |
| std::vector< Real > & | probabilities | |||
| ) | const |
Integral over the density
of M and a one-dimensional function
of conditional probabilities related to the input vector of probabilities p:
| Distribution integral | ( | const F & | f, | |
| const std::vector< Real > & | nominals, | |||
| const std::vector< Real > & | probabilities | |||
| ) | const |
Integral over the density
of M and a multi-dimensional function
of conditional probabilities related to the input vector of probabilities p:
| int checkMoments | ( | Real | tolerance | ) | const |
Check moments (unit norm, zero mean and unit variance) of the distributions of M, Z, and Y by numerically integrating the respective density. Parameter tolerance is the maximum tolerable absolute error.