A WIND-DEPENDENT SELF-EXCITING ELECTRICITY SPOT PRICE MODEL

We present a new electricity spot price model, wherein the prices explicitly depend on the realized wind power production. The proposed geometric approach captures numerous stylized facts of empirical spot price behavior like seasonal variations, time-dependent volatilities, mean-reversion to a stochastically-varying periodic function, price jumps with time-dependent amplitudes, as well as heavy-tailed return distributions. In our setup, the wind power production is modeled by an exogenous self-exciting stochastic process which is independent of the electricity spot price. Though being mathematically uncorrelated, the spot price and the wind power production index behave like negatively correlated entities. Under this self-exciting approach, we deduce a pricing formula for an electricity forward and infer its risk-neutral martingale dynamics.