A Self-Consistent Model for the Forward Price Dynamics

We consider mean-reverting stochastic processes and build a self- consistent model for forward price dynamics and their applications in power industries. This model with stochastic volatility of the forward price is built using the ideas and equations of stochastic differential geometry in order to close the system of equations for the forward price and its volatility. Stationary distributions for the forward price volatility are found analytically as well as the forward price curves in the one factor case. We consider two models for regular forward price volatility. 1)Pure exponential two parameter model with zero asymptotic. 2)Three parameter exponential model with non-zero asymptotic. The first model is a toy one although it can be used in the case of long terms, the second one is quite reliable for short terms. Those models will also play a role of initial conditions for a stochastic process described forward price volatility. We compare our results with those known from the literature.