A Kalman filtering approach to the detection of option mispricing in electric power markets

Abstract

Option pricing models are usually described with the use of stochastic differential equations and diffusion-type partial differential equations (e.g. Black-Scholes models). In case of electric power markets these models are complemented with integral terms which describe the effects of jumps and changes in the diffusion process and which are associated with variations in the production rates, condition of the transmission and distribution system, pay-off capability, etc. Considering the latter case, that is a partial integrodifferential equation for the option's price, a new filtering method is developed for estimating option prices variations without knowledge of initial conditions. The proposed filtering method is the so-called Derivative-free nonlinear Kalman Filter and is based on a transformation of the initial option price dynamics into a state-space model of the linear canonical form. The transformation is shown to be in accordance to differential flatness theory and finally provides a model of the option price dynamics for which state estimation is possible by applying the standard Kalman Filter recursion. Based on the provided state estimate, validation of the Black-Scholes partial integrodifferential equation can be performed and the existence of inconsistent parameters in the electricity market pricing model can be concluded.