An Extended Multi-Factor Structural Model for the Electricity Market

Abstract

This paper proposes an extended version of the analytical structural model for the electricity market developed in a previous paper. The presented electricity price process is driven by stochastic load and random plant availability as well as stochastic marginal generation cost factors embedded in an N-fuel stack framework covering the entire fuel switch dynamics (esp. for N > 2). Potential downside or upside price excursions in variation from the marginal cost level are included via a reserve margin-dependent adjustment function. Presuming a normal or, alternatively, a log-normal fuel price process framework, closed-form expressions for the forward expectation of the electricity price process, for European options premiums, as well as for probabilities and transition probabilities are compiled. The proposed methodology extends the existing structural model universe to the general case of an N-dimensional technology stack including random production defaults as well as reserve margin-driven price adjustments, whilst preserving analytical tractability. Thereby, this completely stochastic framework provides a closed-form model for asset valuation and scenario analysis against the background of electricity markets with an abritrary number N of fuels in the commodity stack. All analytical formulas are obtained using a technique, referred to as the truncated moment generating function method. Based on this generalised moment generating function technique, we are able to derive closed formulas in a very efficient and natural way. Additionally, this approach opens the door to further analytical model extensions. As an example application, we exhibit the assessment of a combined heat and power (CHP) generation unit in a fictitious market environment with a five technology generation stack (N=5).