Lgm1fParametrization< TS > Class Template Reference

LGM 1F Parametrization. More...

#include <qle/models/irlgm1fparametrization.hpp>

Inheritance diagram for Lgm1fParametrization< TS >:

Collaboration diagram for Lgm1fParametrization< TS >:

Public Member Functions
	Lgm1fParametrization (const Currency &currency, const Handle< TS > &termStructure, const std::string &name=std::string())
virtual Real	zeta (const Time t) const =0
virtual Real	H (const Time t) const =0
virtual Real	alpha (const Time t) const
virtual Real	kappa (const Time t) const
virtual Real	Hprime (const Time t) const
virtual Real	Hprime2 (const Time t) const
virtual Real	hullWhiteSigma (const Time t) const
const Handle< TS >	termStructure () const
Real	zetan (const Size n, const Time t, const QuantLib::ext::shared_ptr< Integrator > &integrator)
Real &	shift ()
Real &	scaling ()
Size	numberOfParameters () const override
void	update () const override
Public Member Functions inherited from Parametrization
	Parametrization (const Currency &currency, const std::string &name="")
virtual	~Parametrization ()
virtual const Currency &	currency () const
virtual const Array &	parameterTimes (const Size) const
virtual Size	numberOfParameters () const
virtual Array	parameterValues (const Size) const
virtual const QuantLib::ext::shared_ptr< Parameter >	parameter (const Size) const
virtual void	update () const
const std::string &	name () const
virtual Real	direct (const Size, const Real x) const
virtual Real	inverse (const Size, const Real y) const

Protected Attributes
Real	shift_
Real	scaling_
Protected Attributes inherited from Parametrization
const Real	h_
const Real	h2_

Private Attributes
const Handle< TS >	termStructure_
std::map< std::pair< Size, Real >, Real >	zetan_cached_

Additional Inherited Members
Protected Member Functions inherited from Parametrization
Time	tr (const Time t) const
Time	tl (const Time t) const
Time	tr2 (const Time t) const
Time	tm2 (const Time t) const
Time	tl2 (const Time t) const

Detailed Description

template<class TS>
class QuantExt::Lgm1fParametrization< TS >

LGM 1F Parametrization.

Definition at line 40 of file irlgm1fparametrization.hpp.

Constructor & Destructor Documentation

Lgm1fParametrization()

Lgm1fParametrization	(	const Currency &	currency,
		const Handle< TS > &	termStructure,
		const std::string &	name = std::string()
	)

Definition at line 82 of file irlgm1fparametrization.hpp.

    : Parametrization(currency, name.empty() ? currency.code() : name), shift_(0.0), scaling_(1.0),
      termStructure_(termStructure) {}

Member Function Documentation

zeta()

virtual Real zeta ( const Time  t ) const

pure virtual

zeta must satisfy zeta(0) = 0, zeta'(t) >= 0

Implemented in Lgm1fConstantParametrization< TS >, Lgm1fPiecewiseConstantHullWhiteAdaptor< TS >, Lgm1fPiecewiseConstantParametrization< TS >, and Lgm1fPiecewiseLinearParametrization< TS >.

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H()

virtual Real H ( const Time  t ) const

pure virtual

H must be such that H' does not change its sign

Implemented in Lgm1fConstantParametrization< TS >, Lgm1fPiecewiseConstantHullWhiteAdaptor< TS >, Lgm1fPiecewiseConstantParametrization< TS >, and Lgm1fPiecewiseLinearParametrization< TS >.

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alpha()

Real alpha ( const Time  t ) const

virtual

Reimplemented in Lgm1fConstantParametrization< TS >, Lgm1fPiecewiseConstantHullWhiteAdaptor< TS >, Lgm1fPiecewiseConstantParametrization< TS >, and Lgm1fPiecewiseLinearParametrization< TS >.

Definition at line 89 of file irlgm1fparametrization.hpp.

                                                                                  {
    return std::sqrt((zeta(tr(t)) - zeta(tl(t))) / h_) / scaling_;
}

kappa()

Real kappa ( const Time  t ) const

virtual

Reimplemented in Lgm1fConstantParametrization< TS >, Lgm1fPiecewiseConstantHullWhiteAdaptor< TS >, Lgm1fPiecewiseConstantParametrization< TS >, and Lgm1fPiecewiseLinearParametrization< TS >.

Definition at line 105 of file irlgm1fparametrization.hpp.

{ return -Hprime2(t) / Hprime(t); }

Hprime()

Real Hprime ( const Time  t ) const

virtual

Reimplemented in Lgm1fConstantParametrization< TS >, Lgm1fPiecewiseConstantHullWhiteAdaptor< TS >, Lgm1fPiecewiseConstantParametrization< TS >, and Lgm1fPiecewiseLinearParametrization< TS >.

Definition at line 93 of file irlgm1fparametrization.hpp.

                                                                                   {
    return scaling_ * (H(tr(t)) - H(tl(t))) / h_;
}

Hprime2()

Real Hprime2 ( const Time  t ) const

virtual

Reimplemented in Lgm1fConstantParametrization< TS >, Lgm1fPiecewiseConstantHullWhiteAdaptor< TS >, Lgm1fPiecewiseConstantParametrization< TS >, and Lgm1fPiecewiseLinearParametrization< TS >.

Definition at line 97 of file irlgm1fparametrization.hpp.

                                                                                    {
    return scaling_ * (H(tr2(t)) - 2.0 * H(tm2(t)) + H(tl2(t))) / (h2_ * h2_);
}

hullWhiteSigma()

Real hullWhiteSigma ( const Time  t ) const

virtual

Reimplemented in Lgm1fPiecewiseConstantHullWhiteAdaptor< TS >.

Definition at line 101 of file irlgm1fparametrization.hpp.

                                                                                           {
    return Hprime(t) * alpha(t);
}

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termStructure()

const Handle< TS > termStructure

Definition at line 107 of file irlgm1fparametrization.hpp.

{ return termStructure_; }

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zetan()

Real zetan	(	const Size	n,
		const Time	t,
		const QuantLib::ext::shared_ptr< Integrator > &	integrator
	)

\[ \int_0^t alpha^2(u) H^n(u) du \]

Definition at line 114 of file irlgm1fparametrization.hpp.

                                                                                                 {
    auto z = zetan_cached_.find(std::make_pair(n, t));
    if (z == zetan_cached_.end()) {
        std::vector<Real> times;
        for (Size i = 0; i < numberOfParameters(); ++i)
            times.insert(times.end(), parameterTimes(i).begin(), parameterTimes(i).end());
        PiecewiseIntegral pwint(integrator, times, true);
        Real v = pwint([this, n](Real s) { return std::pow(this->alpha(s), 2) * std::pow(this->H(s), n); }, 0.0, t);
        zetan_cached_[std::make_pair(n, t)] = v;
        return v;
    } else {
        return z->second;
    }
}

shift()

Real & shift

allows to apply a shift to H (model invariance 1)

Definition at line 109 of file irlgm1fparametrization.hpp.

{ return shift_; }

scaling()

Real & scaling

allows to apply a scaling to H and zeta (model invariance 2), note that if a non unit scaling is provided, then the parameterValues method returns the unscaled alpha, while all other methods return scaled (and shifted) values

Definition at line 111 of file irlgm1fparametrization.hpp.

{ return scaling_; }

numberOfParameters()

Size numberOfParameters ( ) const

overridevirtual

the number of parameters in this parametrization

Reimplemented from Parametrization.

Definition at line 67 of file irlgm1fparametrization.hpp.

{ return 2; }

update()

void update

overridevirtual

this method should be called when input parameters linked via references or pointers change in order to ensure consistent results

Reimplemented from Parametrization.

Reimplemented in Lgm1fPiecewiseConstantHullWhiteAdaptor< TS >, Lgm1fPiecewiseConstantParametrization< TS >, and Lgm1fPiecewiseLinearParametrization< TS >.

Definition at line 130 of file irlgm1fparametrization.hpp.

                                                                       {
    Parametrization::update();
    zetan_cached_.clear();
}

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Member Data Documentation

shift_

Real shift_

protected

Definition at line 72 of file irlgm1fparametrization.hpp.

scaling_

Real scaling_

protected

Definition at line 72 of file irlgm1fparametrization.hpp.

termStructure_

const Handle<TS> termStructure_

private

Definition at line 75 of file irlgm1fparametrization.hpp.

zetan_cached_

std::map<std::pair<Size, Real>, Real> zetan_cached_

mutableprivate

Definition at line 76 of file irlgm1fparametrization.hpp.