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Arbitrage-Free Shifting of Price Forward Curves - An Efficient and Generic Algorithm

The most basic and important object for any company trading energy commodities is a so-called Price Forward Curve, or PFC, providing prices in a fine granularity for a future period of time. Clearly, the PFC must be free of arbitrage with respect to the relevant set of forward prices at all times as it is used very frequently and in many different places in a company. Thus, there is need for a fully generic and efficient algorithm producing this arbitrage-free forward curve - a subject yet uncovered by the literature. The algorithm presented in this paper uses techniques from linear algebra and we demonstrate how typical problems and issues from practice such as complicated calendar arithmetics, incorporating bid/ask prices and interplay with Monte-Carlo frameworks are covered. Furthermore, as a by-product, the algorithm produces matrices that allow to change freely between two fundamental representation of the energy market at hand - one being the space of observed forward products, the other being a synthetic world that eases greatly calculations such as pricing, hedging and risk management.