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

17 Pages Posted: 22 Dec 2015

Date Written: July 17, 2015

Abstract

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.

Keywords: Price Forward Curves (PFC), energy markets, electricity markets, arbitrage free pricing, Monte-Carlo methods

JEL Classification: C63, G12, Q40

Suggested Citation

Biegler-König, Richard and Pilz, Kay F., Arbitrage-Free Shifting of Price Forward Curves - An Efficient and Generic Algorithm (July 17, 2015). Available at SSRN: https://ssrn.com/abstract=2706366 or http://dx.doi.org/10.2139/ssrn.2706366

Richard Biegler-König (Contact Author)

STEAG GmbH ( email )

Rellinghauser Str. 1-3
Essen, 45128
Germany

Kay F. Pilz

kinetic mind GmbH ( email )

Sodener Strasse 42
Kelkheim, 65779
Germany

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