KlugeExtOUProcess Class Reference

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

Inheritance diagram for KlugeExtOUProcess:

List of all members.

Public Member Functions

 KlugeExtOUProcess (Real rho, const boost::shared_ptr< ExtOUWithJumpsProcess > &kluge, const boost::shared_ptr< ExtendedOrnsteinUhlenbeckProcess > &extOU)
Size size () const
 returns the number of dimensions of the stochastic process
Size factors () const
 returns the number of independent factors of the process
Disposable< ArrayinitialValues () const
 returns the initial values of the state variables
Disposable< Arraydrift (Time t, const Array &x) const
 returns the drift part of the equation, i.e., $ \mu(t, \mathrm{x}_t) $
Disposable< Matrixdiffusion (Time t, const Array &x) const
 returns the diffusion part of the equation, i.e. $ \sigma(t, \mathrm{x}_t) $
Disposable< Arrayevolve (Time t0, const Array &x0, Time dt, const Array &dw) const
boost::shared_ptr
< ExtOUWithJumpsProcess
getKlugeProcess () const
boost::shared_ptr
< ExtendedOrnsteinUhlenbeckProcess
getExtOUProcess () const
Real rho () const

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

Disposable<Array> evolve ( Time  t0,
const Array x0,
Time  dt,
const Array dw 
) const [virtual]

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.