Arbitrage free cointegrated models in gas and oil future markets

Grégory Benmenzer, Emmanuel Gobet () and Céline Jérusalem
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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

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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.

Keywords: future prices; natural gas; crude oil; cointegration; Vectorial Error Correction Model; arbitrage free modelling (search for similar items in EconPapers)
Date: 2007-12-20
Note: View the original document on HAL open archive server: https://hal.science/hal-00200422v1
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