CommoditySchwartzPiecewiseConstantParametrization Class Reference

COM Schwartz parametrization. More...

#include <qle/models/commodityschwartzpiecewiseconstantparametrization.hpp>

Inheritance diagram for CommoditySchwartzPiecewiseConstantParametrization:

Public Member Functions
	CommoditySchwartzPiecewiseConstantParametrization (const Currency &currency, const std::string &name, const Handle< QuantExt::PriceTermStructure > &priceCurve, const Handle< Quote > &fxSpotToday, const Real sigma, const Real kappa, const Array &aTimes, const Array &a, const QuantLib::ext::shared_ptr< QuantLib::Constraint > &aConstraint=QuantLib::ext::make_shared< QuantLib::NoConstraint >(), bool driftFreeState=false)
Real	variance (const Time t) const override
	State variable variance on [0, t].
Real	sigma (const Time t) const override
	State variable Y's diffusion at time t: sigma * exp(kappa * t).
Real	sigmaParameter () const override
	Inspector for the current value of model parameter sigma (direct).
Real	kappaParameter () const override
	Inspector for the current value of model parameter kappa (direct).
Real	a (const QuantLib::Time t) const override
	Inspector for the current value of model parameter a(T) (direct).
Real	m (const QuantLib::Time t) const override
	Inspector for the current value of model parameter m(T):= exp(a(T)) (direct).
Real	VtT (Real t, Real T) override
	Variance V(t,T) used in the computation of F(t,T).
const QuantLib::ext::shared_ptr< Parameter >	parameter (const Size) const override
	Inspector for current value of the model parameter vector (inverse values).
const Array &	parameterTimes (const Size i) const override
	Inspector for parameter time grid.
void	update () const override
Public Member Functions inherited from CommoditySchwartzParametrization
	CommoditySchwartzParametrization (const Currency &currency, const std::string &name, const Handle< QuantExt::PriceTermStructure > &priceCurve, const Handle< Quote > &fxSpotToday, bool driftFreeState=false)
Size	numberOfParameters () const override
Handle< QuantExt::PriceTermStructure >	priceCurve () const
const Handle< Quote >	fxSpotToday () const
bool	driftFreeState () const
Public Member Functions inherited from Parametrization
	Parametrization (const Currency &currency, const std::string &name="")
virtual const Currency &	currency () const
virtual Array	parameterValues (const Size) const
const std::string &	name () const

Protected Member Functions
Real	direct (const Size i, const Real x) const override
Real	inverse (const Size i, const Real y) const override
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

Protected Attributes
const QuantLib::ext::shared_ptr< PseudoParameter >	sigma_
const QuantLib::ext::shared_ptr< PseudoParameter >	kappa_
Protected Attributes inherited from CommoditySchwartzParametrization
const Handle< QuantExt::PriceTermStructure >	priceCurve_
const Handle< Quote >	fxSpotToday_
std::string	comName_
bool	driftFreeState_
Protected Attributes inherited from Parametrization
const Real	h_
const Real	h2_

Detailed Description

COM Schwartz parametrization.

COM parametrization for the Schwartz (1997) mean-reverting one-factor model with log-normal forward price dynamics and forward volatility sigma * exp(-kappa*(T-t)): dF(t,T) / F(t,T) = exp(b(T)) * sigma * exp(-kappa * (T-t)) * dW
where b is a piecewise constant seasonality adjustment factor.

The model can be propagated in terms of an artificial spot price process of the form S(t) = A(t) * exp(B(t) * X(t)) where
dX(t) = -kappa * X(t) * dt + sigma * dW(t) X(t) - X(s) = -X(s) * (1 - exp(-kappa*(t-s)) + int_s^t sigma * exp(-kappa*(t-u)) dW(u) E[X(t)|s] = X(s) * exp(-kappa*(t-s)) Var[X(t)-X(s)|s] = sigma^2 * (1 - exp(-2*kappa*(t-s))) / (2*kappa)

The stochastic future price curve in terms of X(t) is F(t,T) = F(0,T) * exp(b(T)) * exp( X(t) * exp(-kappa*(T-t) - 1/2 * (V(0,T) - V(t,T)) with V(t,T) = sigma^2 * exp(b(T)) (1 - exp(-2*kappa(T-t))) / (2*kappa) and Var[ln F(T,T)] = VaR[X(T)]

Instead of state variable X we can use Y(t) = exp(kappa * t) * X(t) with drift-free dY(t) = sigma * exp(kappa * t) * dW Y(t) = int_0^t sigma * exp(kappa * s) * dW(s) Var[Y(t)] = sigma^2 * (exp(2*kappa*t) - 1) / (2*kappa) Var[Y(t)-Y(s)|s] = int_s^t sigma * exp(kappa * u) * dW(u) = Var[Y(t)] - Var[Y(s)] The stochastic future price curve in terms of Y(t) is F(t,T) = F(0,t) * exp( Y(t) * exp(-kappa*T) - 1/2 * (V(0,T) - V(t,T))

Constructor & Destructor Documentation

CommoditySchwartzPiecewiseConstantParametrization()

CommoditySchwartzPiecewiseConstantParametrization	(	const Currency &	currency,
		const std::string &	name,
		const Handle< QuantExt::PriceTermStructure > &	priceCurve,
		const Handle< Quote > &	fxSpotToday,
		const Real	sigma,
		const Real	kappa,
		const Array &	aTimes,
		const Array &	a,
		const QuantLib::ext::shared_ptr< QuantLib::Constraint > &	aConstraint = QuantLib::ext::make_shared< QuantLib::NoConstraint >(),
		bool	driftFreeState = false )

The currency refers to the commodity currency, the fx spot is as of today (i.e. the discounted spot)

Member Function Documentation

variance()

Real variance ( const Time t ) const

overridevirtual

State variable variance on [0, t].

Implements CommoditySchwartzParametrization.

sigma()

Real sigma ( const Time t ) const

overridevirtual

State variable Y's diffusion at time t: sigma * exp(kappa * t).

Implements CommoditySchwartzParametrization.

sigmaParameter()

Real sigmaParameter ( ) const

overridevirtual

Inspector for the current value of model parameter sigma (direct).

Implements CommoditySchwartzParametrization.

kappaParameter()

Real kappaParameter ( ) const

overridevirtual

Inspector for the current value of model parameter kappa (direct).

Implements CommoditySchwartzParametrization.

a()

Real a ( const QuantLib::Time t ) const

overridevirtual

Inspector for the current value of model parameter a(T) (direct).

Implements CommoditySchwartzParametrization.

m()

Real m ( const QuantLib::Time t ) const

overridevirtual

Inspector for the current value of model parameter m(T):= exp(a(T)) (direct).

Implements CommoditySchwartzParametrization.

VtT()

Real VtT ( Real t, Real T )

overridevirtual

Variance V(t,T) used in the computation of F(t,T).

Implements CommoditySchwartzParametrization.

parameter()

const QuantLib::ext::shared_ptr< Parameter > parameter ( const Size i ) const

overridevirtual

Inspector for current value of the model parameter vector (inverse values).

Reimplemented from Parametrization.

parameterTimes()

const Array & parameterTimes ( const Size i ) const

overridevirtual

Inspector for parameter time grid.

Reimplemented from Parametrization.

update()

void update ( ) const

overridevirtual

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

Reimplemented from Parametrization.

direct()

Real direct ( const Size , const Real x ) const

overrideprotectedvirtual

transformations between raw and actual parameters

Reimplemented from Parametrization.

inverse()

Real inverse ( const Size i, const Real y ) const

overrideprotectedvirtual

Reimplemented from Parametrization.