ExtOUWithJumpsProcess Class Reference

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

Inheritance diagram for ExtOUWithJumpsProcess:

List of all members.

Public Member Functions

 ExtOUWithJumpsProcess (const boost::shared_ptr< ExtendedOrnsteinUhlenbeckProcess > &process, Real Y0, Real beta, Real jumpIntensity, Real eta)
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
< ExtendedOrnsteinUhlenbeckProcess
getExtendedOrnsteinUhlenbeckProcess () const
Real beta () const
Real eta () const
Real jumpIntensity () const

Detailed Description

This class describes a Ornstein Uhlenbeck model plus exp jump, an extension of the Lucia and Schwartz model

\[ \begin{array}{rcl} S &=& exp(X_t + Y_t) \\ dX_t &=& \alpha(\mu(t)-X_t)dt + \sigma dW_t \\ dY_t &=& -\beta Y_{t-}dt + J_tdN_t \\ \omega(J)&=& \eta_u e^{-\eta_u J} \end{array} \]

References: T. Kluge, 2008. Pricing Swing Options and other Electricity Derivatives, http://eprints.maths.ox.ac.uk/246/1/kluge.pdf

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.