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Optimal dynamic hedging in incomplete futures markets |
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| Authors: | Abraham Lioui Pascal Nguyen Duc Trong Patrice Poncet |
| Institution: | 1. Département Finance, University of Paris-I Sorbonne and Bar Ilan University, Avenue Bernard Hirsch, B.P. 105, 95021, Cergy-Pontoise Cedex, France 2. Département Finance, ESSEC and Université du Littoral, Avenue Bernard Hirsch, B.P. 105, 95021, Cergy-Pontoise Cedex, France 3. Département Finance, University of Paris-I Sorbonne and ESSEC, Avenue Bernard Hirsch, B.P. 105, 95021, Cergy-Pontoise Cedex, France |
| Abstract: | This article derives optimal hedging demands for futures contracts from an investor who cannot freely trade his portfolio of primitive assets in the context of either a CARA or a logarithmic utility function. Existing futures contracts are not numerous enough to complete the market. In addition, in the case of CARA, the nonnegativity constraint on wealth is binding, and the optimal hedging demands are not identical to those that would be derived if the constraint were ignored. Fictitiously completing the market, we can characterize the optimal hedging demands for futures contracts. Closed-form solutions exist in the logarithmic case but not in the CARA case, since then a put (insurance) written on his wealth is implicitly bought by the investor. Although solutions are formally similar to those that obtain under complete markets, incompleteness leads in fact to second-best optima. |
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