2007/12/20 by Grégory Benmenzer, Benmenzer, Grégory, Emmanuel Gobet +3
Economics, Econometrics and Finance · Mathematics · #FOS: Economics and business #FOS: Mathematics #Global Financial Crisis and Policies #Market Dynamics and Volatility #Monetary Policy and Economic Impact #Probability (math.PR) #Risk Management (q-fin.RM) #Statistical Finance (q-fin.ST) #math.PR #q-fin.RM #q-fin.ST
paper · pdf · doi:10.48550/arxiv.0712.3537
arxiv created 2007/12/20 · openalex publication_date 2007/12/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.