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 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