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Arbitrage free cointegrated models in gas and oil future markets

Author

Listed:
  • Grégory Benmenzer

    (GDF Suez - Gaz de France Suez)

  • Emmanuel Gobet

    (MATHFI - Mathématiques financières - LJK - Laboratoire Jean Kuntzmann - UPMF - Université Pierre Mendès France - Grenoble 2 - UJF - Université Joseph Fourier - Grenoble 1 - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - CNRS - Centre National de la Recherche Scientifique)

  • Céline Jérusalem

    (GDF Suez - Gaz de France Suez)

Abstract

In this article we present a continuous time model for natural gas and crude oil future prices. Its main feature is the possibility to link both energies in the long term and in the short term. For each energy, the future returns are represented as the sum of volatility functions driven by motions. Under the risk neutral probability, the motions of both energies are correlated Brownian motions while under the historical probability, they are cointegrated by a Vectorial Error Correction Model. Our approach is equivalent to defining the market price of risk. This model is free of arbitrage: thus, it can be used for risk management as well for option pricing issues. Calibration on European market data and numerical simulations illustrate well its behavior.

Suggested Citation

  • Grégory Benmenzer & Emmanuel Gobet & Céline Jérusalem, 2007. "Arbitrage free cointegrated models in gas and oil future markets," Working Papers hal-00200422, HAL.
    • Handle: RePEc:hal:wpaper:hal-00200422
    Note: View the original document on HAL open archive server: https://hal.science/hal-00200422
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    Cited by:

    1. Kato, Kensuke & Nakamura, Nobuhiro, 2023. "Cointegration analysis of hazard rates and CDSs: Applications to pairs trading strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 612(C).
    2. René Aïd & Luciano Campi & Nicolas Langrené, 2010. "A structural risk-neutral model for pricing and hedging power derivatives," Working Papers hal-00525800, HAL.
    3. Ren'e Aid & Luciano Campi & Nicolas Langren'e & Huy^en Pham, 2012. "A probabilistic numerical method for optimal multiple switching problem and application to investments in electricity generation," Papers 1210.8175, arXiv.org.
    4. René Aïd & Luciano Campi & Nicolas Langrené & Huyên Pham, 2012. "A probabilistic numerical method for optimal multiple switching problems in high dimension," Working Papers hal-00747229, HAL.
    5. Hendrik Kohrs & Hermann Mühlichen & Benjamin R. Auer & Frank Schuhmacher, 2019. "Pricing and risk of swing contracts in natural gas markets," Review of Derivatives Research, Springer, vol. 22(1), pages 77-167, April.
    6. Aïd, René & Campi, Luciano & Langrené, Nicolas & Pham, Huyên, 2014. "A probabilistic numerical method for optimal multiple switching problems in high dimension," LSE Research Online Documents on Economics 63011, London School of Economics and Political Science, LSE Library.

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