摘要翻译：
本文提出了天然气和原油期货价格的连续时间模型。它的主要特点是有可能将长期和短期的能量联系起来。对于每一种能量，未来收益表示为由运动驱动的波动函数之和。在风险中性概率下，两种能量的运动是相关的布朗运动；在历史概率下，两种能量的运动通过向量误差修正模型协整。我们的方法相当于定义了风险的市场价格。该模型不存在套利问题，因此可以用于风险管理，也可以用于期权定价问题。对欧洲市场数据的校正和数值模拟很好地说明了它的行为。
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英文标题：
《Arbitrage free cointegrated models in gas and oil future markets》
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作者：
Gr\'egory Benmenzer (LJK), Emmanuel Gobet (LJK), C\'eline J\'erusalem
  (LJK)
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最新提交年份：
2007
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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英文摘要：
  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.
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PDF链接：
https://arxiv.org/pdf/0712.3537