#include <ql/experimental/processes/klugeextouprocess.hpp>
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< 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< ExtOUWithJumpsProcess > | getKlugeProcess () const |
boost::shared_ptr< ExtendedOrnsteinUhlenbeckProcess > | getExtOUProcess () const |
Real | rho () const |
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virtual Disposable< Array > | expectation (Time t0, const Array &x0, Time dt) const |
virtual Disposable< Matrix > | stdDeviation (Time t0, const Array &x0, Time dt) const |
virtual Disposable< Matrix > | covariance (Time t0, const Array &x0, Time dt) const |
virtual Disposable< Array > | apply (const Array &x0, const Array &dx) const |
virtual Time | time (const Date &) const |
void | update () |
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Observer (const Observer &) | |
Observer & | operator= (const Observer &) |
std::pair< std::set< boost::shared_ptr< Observable > >::iterator, bool > | registerWith (const boost::shared_ptr< Observable > &) |
void | registerWithObservables (const boost::shared_ptr< Observer > &) |
Size | unregisterWith (const boost::shared_ptr< Observable > &) |
void | unregisterWithAll () |
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Observable (const Observable &) | |
Observable & | operator= (const Observable &) |
void | notifyObservers () |
Additional Inherited Members | |
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StochasticProcess (const boost::shared_ptr< discretization > &) | |
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boost::shared_ptr< discretization > | discretization_ |
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
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.