Parameterized Calendar Correlations: Decoding Oil and Beyond

Abstract

We 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. We 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. We apply our model to price a typical commodity derivative, subject to calendar correlations, like an oil swaption. Beyond oil, we investigate the case of natural gas calendar correlations, as well as Eurodollar futures.

TOPICS: Commodities, derivatives, statistical methods

Key Findings

• • We 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 paper.

• • 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.