KlugeExtOUProcess Class Reference

#include <ql/experimental/processes/klugeextouprocess.hpp>

Inheritance diagram for KlugeExtOUProcess:

Public Member Functions
	KlugeExtOUProcess (Real rho, ext::shared_ptr< ExtOUWithJumpsProcess > kluge, ext::shared_ptr< ExtendedOrnsteinUhlenbeckProcess > extOU)
Size	size () const override
	returns the number of dimensions of the stochastic process
Size	factors () const override
	returns the number of independent factors of the process
Array	initialValues () const override
	returns the initial values of the state variables
Array	drift (Time t, const Array &x) const override
	returns the drift part of the equation, i.e., \( \mu(t, \mathrm{x}_t) \)
Matrix	diffusion (Time t, const Array &x) const override
	returns the diffusion part of the equation, i.e. \( \sigma(t, \mathrm{x}_t) \)
Array	evolve (Time t0, const Array &x0, Time dt, const Array &dw) const override
ext::shared_ptr< ExtOUWithJumpsProcess >	getKlugeProcess () const
ext::shared_ptr< ExtendedOrnsteinUhlenbeckProcess >	getExtOUProcess () const
Real	rho () const
Public Member Functions inherited from StochasticProcess
virtual Array	expectation (Time t0, const Array &x0, Time dt) const
virtual Matrix	stdDeviation (Time t0, const Array &x0, Time dt) const
virtual Matrix	covariance (Time t0, const Array &x0, Time dt) const
virtual Array	apply (const Array &x0, const Array &dx) const
virtual Time	time (const Date &) const
void	update () override
Public Member Functions inherited from Observer
	Observer (const Observer &)
Observer &	operator= (const Observer &)
std::pair< iterator, bool >	registerWith (const ext::shared_ptr< Observable > &)
void	registerWithObservables (const ext::shared_ptr< Observer > &)
Size	unregisterWith (const ext::shared_ptr< Observable > &)
void	unregisterWithAll ()
virtual void	deepUpdate ()
Public Member Functions inherited from Observable
	Observable (const Observable &)
Observable &	operator= (const Observable &)
	Observable (Observable &&)=delete
Observable &	operator= (Observable &&)=delete
void	notifyObservers ()

Additional Inherited Members
Public Types inherited from Observer
typedef set_type::iterator	iterator
	StochasticProcess (ext::shared_ptr< discretization >)
ext::shared_ptr< discretization >	discretization_

Detailed Description

This class describes a correlated Kluge - extended Ornstein-Uhlenbeck process governed by

\[\begin{array}{rcl} P_t &=& \exp(p_t + X_t + Y_t) \\ dX_t &=& -\alpha X_tdt + \sigma_x dW_t^x \\ dY_t &=& -\beta Y_{t-}dt + J_tdN_t \\ \omega(J) &=& \eta e^{-\eta J} \\ G_t &=& \exp(g_t + U_t) \\ dU_t &=& -\kappa U_tdt + \sigma_udW_t^u \\ \rho &=& \mathrm{corr} (dW_t^x, dW_t^u) \end{array} \]

References: B. Hambly, S. Howison, T. Kluge, Modelling spikes and pricing swing options in electricity markets, http://people.maths.ox.ac.uk/hambly/PDF/Papers/elec.pdf

Member Function Documentation

size()

Size size ( ) const

overridevirtual

returns the number of dimensions of the stochastic process

Implements StochasticProcess.

factors()

Size factors ( ) const

overridevirtual

returns the number of independent factors of the process

Reimplemented from StochasticProcess.

initialValues()

Array initialValues ( ) const

overridevirtual

returns the initial values of the state variables

Implements StochasticProcess.

drift()

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

overridevirtual

returns the drift part of the equation, i.e., \( \mu(t, \mathrm{x}_t) \)

Implements StochasticProcess.

diffusion()

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

overridevirtual

returns the diffusion part of the equation, i.e. \( \sigma(t, \mathrm{x}_t) \)

Implements StochasticProcess.

evolve()

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

overridevirtual

returns the asset value after a time interval \( \Delta t \) according to the given discretization. By default, it returns

\[E(\mathrm{x}_0,t_0,\Delta t) + S(\mathrm{x}_0,t_0,\Delta t) \cdot \Delta \mathrm{w} \]

where \( E \) is the expectation and \( S \) the standard deviation.

Reimplemented from StochasticProcess.