COM Schwartz parametrization. More...

#include <qle/models/commodityschwartzparametrization.hpp>

Inheritance diagram for CommoditySchwartzParametrization:

Public Member Functions
	CommoditySchwartzParametrization (const Currency &currency, const std::string &name, const Handle< QuantExt::PriceTermStructure > &priceCurve, const Handle< Quote > &fxSpotToday, const Real sigma, const Real kappa, bool driftFreeState=false)

Size	numberOfParameters () const override

Real	variance (const Time t) const
	State variable variance on [0, t].

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

Real	sigmaParameter () const
	Inspector for the current value of model parameter sigma (direct)

Real	kappaParameter () const
	Inspector for the current value of model parameter kappa (direct)

const boost::shared_ptr< Parameter >	parameter (const Size) const override
	Inspector for current value of the model parameter vector (inverse values)

Handle< QuantExt::PriceTermStructure >	priceCurve ()
	Inspector for today's price curve.

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

bool	driftFreeState () const

Public Member Functions inherited from Parametrization
	Parametrization (const Currency &currency, const std::string &name="")

virtual const Currency &	currency () const

virtual const Array &	parameterTimes (const Size) const

virtual Array	parameterValues (const Size) const

virtual void	update () 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

Additional Inherited Members
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) = sigma * exp(-kappa * (T-t)) * dW

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( X(t) * exp(-kappa*(T-t) - 1/2 * (V(0,T) - V(t,T)) with V(t,T) = sigma^2 * (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

◆ CommoditySchwartzParametrization()

CommoditySchwartzParametrization	(	const Currency &	currency,
		const std::string &	name,
		const Handle< QuantExt::PriceTermStructure > &	priceCurve,
		const Handle< Quote > &	fxSpotToday,
		const Real	sigma,
		const Real	kappa,
		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

◆ numberOfParameters()

Size numberOfParameters ( ) const

overridevirtual

the number of parameters in this parametrization

Reimplemented from Parametrization.

◆ direct()

Real direct	(	const Size	Size,
		const Real	x
	)		const

overrideprotectedvirtual

transformations between raw and actual parameters