Abstract

One of the main purposes to use the futures products in commodity markets is to fill the hedging needs for relatively large market risk and counterparty risk in commodity spot markets. We believe that these two types of market and credit risk will be incorporated into the commodity futures prices. The paper proposes a price model for commodity futures using a new volatility based convenience yield fluctuation and an interest rate fluctuation, which represent the market and credit risk, respectively, in commodity futures markets at the first order approximation. We offer the additional explanation for commodity futures trades such that the futures trades may be conducted for the mitigation of the large spot price volatility in commodity markets characterized by its mean reversion. It is shown that the market risk model, i.e., the new volatility based convenience yield model, can incorporate the inverse hump shape, which is often observed in commodity markets, into the futures term structure and that the interest rate extended model of the market risk model can enhance the contango shape. Empirical studies are conducted using WTI crude oil, heating oil, and natural gas futures traded on the NYMEX. It is shown that the Samuelson effects for heating oil and natural gas futures are captured for both of the proposed models while the Samuelson effects for the WTI crude oil futures are not relevant. In addition, the market risk model using the estimated parameters can demonstrate the inverse hump shape in the crude oil futures term structure and the inclusion of the interest rate model can enhance the contango shape.

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