returns the covariance $$ V(\mathrm{x}{t_0 + \Delta t} | \mathrm{x}{t_0} = \mathrm{x}_0) $$ of the process after a time interval $ \Delta t $ according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
returns the expectation $$ E(\mathrm{x}{t_0 + \Delta t} | \mathrm{x}{t_0} = \mathrm{x}_0) $$ of the process after a time interval $ \Delta t $ according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
returns the standard deviation $$ S(\mathrm{x}{t_0 + \Delta t} | \mathrm{x}{t_0} = \mathrm{x}_0) $$ of the process after a time interval $ \Delta t $ according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
returns the time value corresponding to the given date in the reference system of the stochastic process.
note As a number of processes might not need this functionality, a default implementation is given which raises an exception.
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