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: Kluge, Timo L., 2008. Pricing Swing Options and other Electricity Derivatives, http://eprints.maths.ox.ac.uk/246/1/kluge.pdf
http://spanderen.de/2011/06/13/vpp-pricing-i-stochastic-processes-partial- integro-differential-equation/
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: Kluge, Timo L., 2008. Pricing Swing Options and other Electricity Derivatives, http://eprints.maths.ox.ac.uk/246/1/kluge.pdf
http://spanderen.de/2011/06/13/vpp-pricing-i-stochastic-processes-partial- integro-differential-equation/