The authors suggest parametric families to model calendar correlations. They capture the empirical properties of historical realized calendar correlations: the growth of correlations with time to the expiration of earlier contract, and decay with time between two contracts. The authors fully investigate surfaces for the minimum eigenvalue of the correlation matrix in the parametric space. The main constituent of the model is the dynamics for instantaneous correlation between two contracts under Samuelson dynamics for volatilities, which allows one to map realized correlations to different time intervals, similar to Samuelson volatility. The fit of the model to the oil case shows excellent results. They apply their model to price a typical commodity derivative, subject to calendar correlations, like an oil swaption. Beyond oil, they investigate the case of natural gas calendar correlations, as well as eurodollar futures. TOPICS: Commodities, derivatives, statistical methods Key Findings • The authors provide a novel two-parameter framework to parameterize calendar correlation matrices for oil futures. This model captures the key fundamental properties of calendar correlations: decay of correlations with time between contracts, and growth for contracts farther away. • The growth of correlations represents the “Samuelson effect” for commodity futures and is captured through dynamics of instantaneous correlations. These dynamics allow one to map correlations to any time interval. This makes the model very efficient in pricing commodity swaptions, which is demonstrated in the article. • Seasonal commodities like natural gas and power present additional challenges. Through the introduction of an additional “storage scaling parameter”, we captured natural gas correlations reasonably well. Beyond commodities, we successfully applied our model to parameterize correlations on eurodollar futures.

中文翻译：

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参数化日历相关性：解码油及其他

作者建议使用参数族来模拟日历相关性。他们捕获了历史实现日历相关性的经验特性：相关性随着时间的增长而增长到较早的合同到期，而两个合同之间的时间则随着时间而衰减。作者充分研究了曲面中参数空间中相关矩阵的最小特征值。该模型的主要组成部分是在Samuelson波动率动力学下的两个合约之间的瞬时关联动力学，它允许将已实现的关联映射到不同的时间间隔，类似于Samuelson波动率。模型与油箱的拟合显示出极好的结果。他们将自己的模型应用于典型商品衍生产品的定价，但要遵循日历相关性，例如石油掉期。除了石油，他们调查了天然气日历相关性以及欧洲美元期货的情况。主题：商品，衍生物，统计方法主要发现•作者提供了一个新颖的两参数框架，用于参数化石油期货的日历相关矩阵。该模型捕获了日历相关性的关键基本属性：随着合同之间的时间相关性的衰减，以及远离合同的合同的增长。•相关性的增长代表商品期货的“萨缪尔森效应”，并通过瞬时相关性的动态来捕捉。这些动力学使人们可以将相关性映射到任何时间间隔。这使得该模型在商品交换定价中非常有效，这在本文中得到了证明。•天然气和电力等季节性商品带来了更多挑战。通过引入额外的“存储比例参数”，我们可以很好地捕获天然气的相关性。除了大宗商品，我们还成功地将我们的模型应用于参数化美元兑欧元期货的相关性。