CrCirppStateProcess Class Reference

CIR++ Model State Process. More...

#include <qle/processes/crcirppstateprocess.hpp>

Inheritance diagram for CrCirppStateProcess:

Collaboration diagram for CrCirppStateProcess:

Public Types
enum	Discretization { BrigoAlfonsi }

Public Member Functions
	CrCirppStateProcess (CrCirpp *const model, CrCirppStateProcess::Discretization disc=CrCirppStateProcess::Discretization::BrigoAlfonsi)
Size	size () const override
Array	initialValues () const override
Array	drift (Time t, const Array &x) const override
Matrix	diffusion (Time t, const Array &x) const override
Array	evolve (Time t0, const Array &x0, Time dt, const Array &dw) const override
const CrCirpp *	model () const
const CrCirppStateProcess::Discretization	discretization ()

Protected Attributes
const CrCirpp *	model_
const CrCirppStateProcess::Discretization	discretization_

Detailed Description

CIR++ Model State Process.

Definition at line 37 of file crcirppstateprocess.hpp.

Member Enumeration Documentation

Discretization

enum Discretization

Enumerator
BrigoAlfonsi

Definition at line 39 of file crcirppstateprocess.hpp.

{ BrigoAlfonsi };

Constructor & Destructor Documentation

CrCirppStateProcess()

CrCirppStateProcess	(	CrCirpp *const	model,
		CrCirppStateProcess::Discretization	disc = CrCirppStateProcess::Discretization::BrigoAlfonsi
	)

Definition at line 28 of file crcirppstateprocess.cpp.

    : StochasticProcess(QuantLib::ext::shared_ptr<StochasticProcess::discretization>(new EulerDiscretization)), model_(model),
      discretization_(disc) {}

Member Function Documentation

size()

Size size ( ) const

override

StochasticProcess interface

Definition at line 33 of file crcirppstateprocess.cpp.

{ return 2; }

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initialValues()

Array initialValues ( ) const

override

Definition at line 35 of file crcirppstateprocess.cpp.

                                               {
    Array res(size(), 0.0);
    res[0] = model_->parametrization()->y0(0); // y0
    res[1] = 1.0; // S(0,0) = 1
    return res;
}

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drift()

Array drift ( Time  t, const Array &  x  ) const

override

Definition at line 42 of file crcirppstateprocess.cpp.

                                                             {
    QL_FAIL("not implemented");
}

diffusion()

Matrix diffusion ( Time  t, const Array &  x  ) const

override

Definition at line 46 of file crcirppstateprocess.cpp.

                                                                  {
    QL_FAIL("not implemented");
}

evolve()

Array evolve ( Time  t0, const Array &  x0, Time  dt, const Array &  dw  ) const

override

Definition at line 50 of file crcirppstateprocess.cpp.

                                                                                          {
    Array retVal(size());
    Real kappa, theta, sigma, y0;
    kappa = model_->parametrization()->kappa(t0);
    theta = model_->parametrization()->theta(t0);
    sigma = model_->parametrization()->sigma(t0);
    y0 = model_->parametrization()->y0(t0);
 
    const Real sdt = std::sqrt(dt);
    switch (discretization_) {
 
    case BrigoAlfonsi: {
        // see D. Brigo and F. Mercurio. Interest Rate Models: Theory and Practice, 2nd
        // Edition. Springer, 2006.
        // Ensures non-negative values for \sigma^2 \leq 2*\kappa*\theta
        Real temp = (1 - kappa / 2.0 * dt);
        Real temp2 = temp * std::sqrt(x0[0]) + sigma * sdt * dw[0] / (2.0 * temp);
        retVal[0] = temp2 * temp2 + (kappa * theta - sigma * sigma / 4) * dt;
        break;
    }
    default:
        QL_FAIL("unknown discretization schema");
    }
 
    // second element is S(0,i)
    Real SM_ti = model_->defaultCurve()->survivalProbability(t0 + dt);
    Real SM_ti_pre = model_->defaultCurve()->survivalProbability(t0);
    Real Pcir_ti = model_->zeroBond(0, t0 + dt, y0);
    Real Pcir_ti_pre = model_->zeroBond(0, t0, y0);
    retVal[1] = x0[1] * SM_ti / SM_ti_pre * Pcir_ti_pre / Pcir_ti * exp(-x0[0] * dt);
 
    return retVal;
}

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model()

const CrCirpp * model

(

)

const

Definition at line 53 of file crcirppstateprocess.hpp.

{ return model_; }

discretization()

const CrCirppStateProcess::Discretization discretization

(

)

Definition at line 54 of file crcirppstateprocess.hpp.

{ return discretization_; }

Member Data Documentation

model_

const CrCirpp* model_

protected

Definition at line 57 of file crcirppstateprocess.hpp.

discretization_

const CrCirppStateProcess::Discretization discretization_

protected

Definition at line 58 of file crcirppstateprocess.hpp.