An excitable stochastic model of electricity prices dynamics

In the last decade some countries decided to undertake a deregulation process of the electricity sector in order to bring competition to the previously monopolistic market. In all those countries electricity is now a traded commodity and its price is determined according to the rule of supply and demand. The empirical analysis reveals that market prices are variable and unpredictable with jumps and pronounced spikes. Figure 1 shows the time evolution of electricity prices at the Amsterdam Power Exchange (APX) and at the Scandinavian Nord Pool Elspot: prices experience normal stable periods in which they fluctuate around some long run average, and turbulent periods in which the dynamics is affected by jumps and short-lived spikes. Several models of electricity prices dynamics have been proposed in literature. Due to their mathematical tractability, single-factor and multi-factor affine diffusion models (Lucia and Schwartz 2002) accounting for the mean-reversion property have been extensively used; to include jumps and spikes, jump-diffusion models (Deng 1999, Escribano, Penã, and Villaplana 2002, Geman and Roncoroni 2003) have been proposed; to distinguish the normal stable motion from the turbulent and spike dynamics, regime-switching models have been introduced (Huisman and Mahieu 2003, de Jong 2005, Mari 2006). The occurrence of spikes in power prices dynamics can be understood if we consider that electricity is a very special commodity: with the exception of hydroelectric power, it cannot be stored and must be generated at the instant it is consumed; the demand is highly inelastic and very sensitive to the temperature; the generation process (supply) is characterized by low marginal costs but, when emergency generators are to be put on operation in order to satisfy the demand, marginal costs may be very high. Prices are therefore very sensitive to the demand, to outages and grid congestions: shortages in electricity generation, forced outages, peaks in electricity demand determine spikes