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Arbitrage free cointegrated models in gas and oil future markets

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  • Gr'egory Benmenzer

    (LJK)

  • Emmanuel Gobet

    (LJK)

  • C'eline J'erusalem

    (LJK)

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

  • Gr'egory Benmenzer & Emmanuel Gobet & C'eline J'erusalem, 2007. "Arbitrage free cointegrated models in gas and oil future markets," Papers 0712.3537, arXiv.org.
    • Handle: RePEc:arx:papers:0712.3537
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    1. repec:clg:wpaper:1999-04 is not listed on IDEAS
    2. Panagiotidis, Theodore & Rutledge, Emilie, 2007. "Oil and gas markets in the UK: Evidence from a cointegrating approach," Energy Economics, Elsevier, vol. 29(2), pages 329-347, March.
    3. repec:dau:papers:123456789/607 is not listed on IDEAS
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    Cited by:

    1. 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.
    2. 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).
    3. 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.
    4. René Aïd & Luciano Campi & Nicolas Langrené, 2010. "A structural risk-neutral model for pricing and hedging power derivatives," Working Papers hal-00525800, HAL.
    5. 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.
    6. 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.

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