Post by Sapphire Capital on Sept 5, 2008 3:38:20 GMT 4
Optimal Dynamic Hedging in Commodity Futures Markets with a Stochastic Convenience Yield
Constantin Mellios
Université Paris I Panthéon-Sorbonne
Pierre Six
August 25, 2008
Abstract:
The main objective of this paper is to fill the gap in the literature by addressing, in a continuous-time context, the issue of using commodity futures as vehicles for hedging purposes when, in particular, the convenience yield as well as the market prices of risk evolve randomly over time. Following the martingale route and by operating a suitable constant relative risk aversion utility function (CRRA) specific change of numeraire, we derive optimal demands for commodity futures contracts by an unconstrained investor, who can freely trade on the underlying spot asset and on a discount bond. Although the optimal demand exhibits a classical structure in that it is composed of a speculative part and of a hedging term, our model has four main distinctive features and goes beyond the existing studies. First, the speculative and hedging components may be decomposed in a convenient way underlining, in particular, the effect of the stochastic behavior of both the market prices of risk and the convenience yield on optimal demands. As a consequence, the investor is able to exactly asses their impact on optimal demands. Second, the interaction between the prices of risk associated especially with the spot commodity and the convenience yield combined with their mean-reverting character determine the sign and the magnitude of the speculative and the hedging proportions. Third, the futures contract turns out to be the appropriate instrument to hedge the idiosyncratic source of risk of the convenience yield. Furthermore, in contrast to Breeden's (1984) results, the primitive assets are effective in hedging the specific risk of the (log) spot commodity and the interest rate. Finally, optimal demands can be computed in a recursive way, which greatly facilitates the use of our model for practical considerations.
papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1254650_code950119.pdf?abstractid=1254650&mirid=2
Constantin Mellios
Université Paris I Panthéon-Sorbonne
Pierre Six
August 25, 2008
Abstract:
The main objective of this paper is to fill the gap in the literature by addressing, in a continuous-time context, the issue of using commodity futures as vehicles for hedging purposes when, in particular, the convenience yield as well as the market prices of risk evolve randomly over time. Following the martingale route and by operating a suitable constant relative risk aversion utility function (CRRA) specific change of numeraire, we derive optimal demands for commodity futures contracts by an unconstrained investor, who can freely trade on the underlying spot asset and on a discount bond. Although the optimal demand exhibits a classical structure in that it is composed of a speculative part and of a hedging term, our model has four main distinctive features and goes beyond the existing studies. First, the speculative and hedging components may be decomposed in a convenient way underlining, in particular, the effect of the stochastic behavior of both the market prices of risk and the convenience yield on optimal demands. As a consequence, the investor is able to exactly asses their impact on optimal demands. Second, the interaction between the prices of risk associated especially with the spot commodity and the convenience yield combined with their mean-reverting character determine the sign and the magnitude of the speculative and the hedging proportions. Third, the futures contract turns out to be the appropriate instrument to hedge the idiosyncratic source of risk of the convenience yield. Furthermore, in contrast to Breeden's (1984) results, the primitive assets are effective in hedging the specific risk of the (log) spot commodity and the interest rate. Finally, optimal demands can be computed in a recursive way, which greatly facilitates the use of our model for practical considerations.
papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1254650_code950119.pdf?abstractid=1254650&mirid=2