Pricing of Forwards and Other Derivatives in Cointegrated Commodity Markets

22 Pages Posted: 28 Oct 2014

See all articles by Fred Espen Benth

Fred Espen Benth

University of Oslo

Steen Koekebakker

School of Business and Law at the University of Agder

Date Written: October 27, 2014

Abstract

We analyse cointegration in commodity markets, and propose a parametric class of pricing measures which preserves cointegration for forward prices with fixed time to maturity. We present explicit expressions for the term structure of volatility and correlation in the context of our spot price models based on continuous-time autoregressive moving average dynamics for the stationary components. The term structures have many interesting shapes, and we provide some empirical evidence from refined oil futures prices at NYMEX defending our modelling idea. Motivated from these results, we present a cointegrated forward price dynamics using the Heath-Jarrow-Morton modelling idea. In this setting, the concept of cointegration is extended to what we call "cointegration in the limit", which is an asymptotic form of the notion. The Margrabe formula for spread option prices is shown to hold, with an explicit plug-in volatility. We present several numerical examples showing that cointegration leads to significantly cheaper spread options compared to the complete market case, where cointegration disappears for the pricing measure.

Keywords: Cointegration, risk premium, CARMA processes, commodity markets, spot and forward relationship, Heath-Jarrow-Morton modeling

JEL Classification: C02, C32, C38, D52, D53, G13

Suggested Citation

Benth, Fred Espen and Koekebakker, Steen, Pricing of Forwards and Other Derivatives in Cointegrated Commodity Markets (October 27, 2014). Available at SSRN: https://ssrn.com/abstract=2515406 or http://dx.doi.org/10.2139/ssrn.2515406

Fred Espen Benth (Contact Author)

University of Oslo ( email )

Center of Mathematics for Applications
Oslo, N-0317
Norway

Steen Koekebakker

School of Business and Law at the University of Agder ( email )

Servicebox 422
Kristiansand, N-4604
Norway
+47 38 14 15 31 (Phone)

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