HAL : hal-00200422, version 1

arXiv : 0712.3537

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Arbitrage free cointegrated models in gas and oil future markets

Grégory Benmenzer 1, Emmanuel Gobet 2, Céline Jérusalem 1

(20/12/2007)

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.

1 :	GDF SUEZ
	Direction de la Recherche - GDF SUEZ
2 :	Laboratoire Jean Kuntzmann (LJK)
	CNRS : UMR5224 – Université Joseph Fourier - Grenoble I – Université Pierre-Mendès-France - Grenoble II – Institut Polytechnique de Grenoble - Grenoble Institute of Technology

Domaine

:

Mathématiques/Probabilités Sciences de l'Homme et Société/Economies et finances

Mots Clés : future prices – natural gas – crude oil – cointegration – Vectorial Error Correction Model – arbitrage free modelling

hal-00200422, version 1

http://hal.archives-ouvertes.fr/hal-00200422

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Contributeur : Emmanuel Gobet <>

Soumis le : Jeudi 20 Décembre 2007, 17:57:58

Dernière modification le : Mercredi 10 Décembre 2008, 18:05:33