Electricity spot market prices are notoriously difficult to model, let alone predict, because of their extreme volatility. Such volatility is reflected in so-called price spikes that may increase the spot price by an order of magnitude as a matter of hours. Spot market price series are also subject to many other types of phenomena, such as periodicities at different scales, and to mean reversion. We introduce a model for electricity spot market prices that includes both spikes and mean reversion. The model is based on a jump diffusion process that is superimposed on a mean reverting Ornstein-Uhlenbeck model. Mean reversion takes place at several different time and price scales, so as to reproduce the observed behavior of spot market prices correctly. The parameters of the model are calibrated with the Nord Pool spot market hourly price series using a maximum likelihood approach. The simulated price series thus obtained very closely follows the statistical characteristics of the real price series.
Purpose -Under the Kyoto protocol, emissions trading was imposed upon the Nordic Nord Pool Spot market in 2005. The purpose of this paper is to identify and characterize an important side-effect of emissions trading on electricity spot market price behavior by statistically comparing price behavior before and after emissions trading was introduced. Design/methodology/approach -The analysis is based on an analysis of the skill of regression models in explaining price behavior before and after 2005. Findings -It turns out that regression models based on background variables such as temperature, water reservoir levels, and even the price of emission rights themselves lose much of their skill from 2005 onwards. The histogram of the residual time series of an optimally calibrated regression model demonstrates a considerably more "fat-tailed" behavior after 2005, with a much higher volatility and reduced amenability for regression by background variables. Practical implications -The results point to an increased medium-and long-term uncertainty in the Nordic electricity spot market, brought about by emissions trading as an unintended side-effect. It seems emissions trading has introduced a stronger "psychological" component into price behavior, increasing its volatility and making it prone to more frequent price spikes. This has made the electricity market more difficult for market managers and regulators to manage. Originality/value -The paper presents the first statistical attempt to quantify the way electricity spot price dynamics have changed in Europe after starting the Emissions Trading Scheme based on the Kyoto protocol.
Collective behavior of herding animals displays a balance between conservative cohesive forces and "'innovation"', or moving towards a goal, as described by Couzin in 2005Couzin in (2005. We have given these forces a quantitative mathematical form that is amenable to numerical simulation. The simulations described herein reproduce the phenomena that Couzin observed and indicate that a nearly 5 per cent critical mass is sufficient to pull the whole population along, but smaller innovative teams fail to attract a substantial following. The resulting non-linear dynamic equations have been applied also to modeling of financial market dynamics, where they are seen to produce financial catastrophes by internal population dynamics alone, without any need for external forcing. The equations can thereby also be interpreted as a model of John Maynard Keynes ' Animal Spirits (1936) that are often evoked to describe market psychology.
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