Power spot price models with negative prices

ABSTRACT Negative prices for electricity are a recent development in European power markets. Negative hourly prices have been permitted at Germany's European Energy Exchange (EEX) spot market since autumn 2008 and have occurred frequently since, reaching values as low as €-500/MWh. However, in some non-European markets such as those in the US, Australia and Canada, negative prices have been observed over longer periods. Negative prices are, in fact, natural in electricity spot trading. Plant flexibility is limited and costly, and, therefore, incurring a negative price for an hour can actually be economically optimal overall. Negative prices pose a basic problem for stochastic price modeling in that going from prices to log prices is not possible. So far, this has been dealt with using "workarounds". In this paper, a thorough approach is advocated, based on the area hyperbolic sine transformation. The transformation is applied to spot modeling of the German EEX and the Electric Reliability Council of Texas's West Texas (ERCOT West) market, and an exemplary valuation of an option is carried out. It is concluded that the area hyperbolic sine transform is a natural starting point for modeling negative power prices. It can be integrated into common stochastic price models without adding much complexity. Moreover, this transformation might, in general, be more appropriate for power prices than the log transformation, considering the fundamentals of power price formation. Negative prices can significantly affect a business and a thorough treatment is therefore indispensable.