Valuation of commodity structures in co-integrated futures markets

In this paper, Dan Mahoney and Krzysztof Wolyniec show that in co-integrated (mean-reverting) futures markets, active dynamic hedging is required to realise the quadratic variation of the underlying spread process. Using static hedges/portfolios yields significantly different values from those available with dynamic strategies no matter what risk adjustment or penalty is adopted. The implications for pricing, hedging and optimal trading strategies in commodity markets are discussed

technical blocks

It is well known that several consumable commodity markets are related through equilibrium mechanisms: either through substitution or complementarity effects. For example, natural gas is used for production of electrical power in the US and UK to such an extent that power price formation is clearly influenced by the behaviour of natural gas prices.

Examples of other related commodities abound: crude oil and gasoline, heating oil and gasoline (substitution on the output side), natural gas and

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