# QuantLib_ExtOUWithJumpsProcess man page

ExtOUWithJumpsProcess

## Synopsis

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

Inherits StochasticProcess.

### 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< Array > initialValues () const
returns the initial values of the state variables
Disposable< Array > drift (Time t, const Array &x) const
returns the drift part of the equation, i.e., \$ mu(t, mathrm{x}_t) \$
Disposable< Matrix > diffusion (Time t, const Array &x) const
returns the diffusion part of the equation, i.e. \$ sigma(t, mathrm{x}_t) \$
Disposable< Array > evolve (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)&=& \ta_u e^{-\ta_u J} \nd{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.

## Author

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## Referenced By

The man pages eta(3), ExtOUWithJumpsProcess(3), getExtendedOrnsteinUhlenbeckProcess(3), initialValues(3) and jumpIntensity(3) are aliases of QuantLib_ExtOUWithJumpsProcess(3).

Wed Feb 7 2018 Version 1.10.1 QuantLib