Pricing electricity forwards under future information on the stochastic mean-reversion level
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Pricing electricity forwards under future information on the stochastic mean-reversion level Markus Hess1 Received: 22 July 2019 / Accepted: 10 September 2020 © Associazione per la Matematica Applicata alle Scienze Economiche e Sociali (AMASES) 2020
Abstract We extend the arithmetic multi-factor electricity spot price model proposed by Benth et al. (Appl Math Finance 14(2):153–169, 2007) by adding stochastic mean-level processes to their model and by taking additional information on the future behavior of these mean-level processes into account. The available anticipative information is modeled by an initially enlarged filtration in our paper. We further derive pricing formulas for electricity forwards under future information and investigate the associated information premium. Keywords Electricity spot/forward/futures price · Arithmetic multi-factor model · Pure-jump Ornstein–Uhlenbeck process · Lévy-type process · Poisson random measure · Stochastic differential equation · Initially enlarged filtration · Information premium Mathematics Subject Classification 60G44 · 60G51 · 60G57 · 60H10 · 91B44 · 91B70 · 91G20 JEL Classification C02 · D43 · D52 · D82 · G13 · G14
1 Introduction Electricity constitutes a so-called flow commodity which cannot be stored (or has at least very limited storage possibilities) and thus, cannot be traded in the usual sense, as conventional buy–hold–sell strategies collapse. As a consequence, electricity price trajectories typically show a strong seasonal component, impressive price spikes as well as mean-reversion to a periodically varying seasonality function [see Fig. 1 in Benth et al. (2007)]. Benth et al. (2007) proposed a tractable spot price model
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Markus Hess [email protected] Frankfurt/Main, Germany
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M. Hess
which is able to capture the mentioned particularities of electricity prices. In the present paper, we extend the arithmetic multi-factor spot price model proposed in Benth et al. (2007) by adding a stochastic mean-level process to the model and by taking additional information on the future behavior of this mean-level process into account. The available future information is modeled by an initially enlarged filtration in our paper. In Aksamit and Jeanblanc (2017), Benth and Meyer-Brandis (2009), Di Nunno et al. (2009), Hess (2013, 2017), numerous arguments that count in favor for an incorporation of anticipative information into mathematical pricing approaches in financial and electricity markets are presented. Typical examples of relevant future information in electricity markets are the introduction of carbon dioxide emission costs, the planned building of physical connections to other electricity markets, the outage of a major power plant, a future promotion of renewable electricity, or other political decisions. Also weather forecasts play an important role, as electricity prices are known to be highly correlated with outdoor temperature. Electricity market models can roughly be divided into spot and forward price models (somehow similarly to short and for
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