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Dynamic Hedging with Stochastic Differential Utility

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  • Bueno, Rodrigo De Losso da Silveira

Abstract

In this paper we study the dynamic hedging problem using three different utility specifications: stochastic differential utility, terminal wealth utility, and a new utility transformation which includes features from the two previous approaches. In all three cases, we assume Markovian prices. While stochastic differential utility (SDU) has an ambiguous effect on the pure hedging demand, it does decrease the pure speculative demand, because risk aversion increases. We also show that in this case the consumption decision is, in some sense, independent of the hedging decision. In the case of terminal wealth utility (TWU), we derive a general and compact hedging formula which nests as special cases all of the models studied in Duffie and Jackson (1990). In the case of the new utility transformation, we find a compact formula for hedging which encompasses the terminal wealth utility framework as a special case; we then show that this specification does not affect the pure hedging demand. In addition, with CRRA- and CARA-type utilities the risk aversion increases, and consequently, the pure speculative demand decreases. If futures prices are martingales, then the transformation plays no role in determining the hedging allocation. Our results hold for a number of different price distributions. We also use semigroup techniques to derive the relevant Bellman equation for each case.

Suggested Citation

  • Bueno, Rodrigo De Losso da Silveira, 2006. "Dynamic Hedging with Stochastic Differential Utility," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 26(2), November.
    • Handle: RePEc:sbe:breart:v:26:y:2006:i:2:a:1579
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    1. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    2. Duffie, Darrel & Lions, Pierre-Louis, 1992. "PDE solutions of stochastic differential utility," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 577-606.
    3. Breeden, Douglas T., 1984. "Futures markets and commodity options: Hedging and optimality in incomplete markets," Journal of Economic Theory, Elsevier, vol. 32(2), pages 275-300, April.
    4. Duffie, Darrell & Jackson, Matthew O., 1990. "Optimal hedging and equilibrium in a dynamic futures market," Journal of Economic Dynamics and Control, Elsevier, vol. 14(1), pages 21-33, February.
    5. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    6. Ronald W. Anderson & Jean-Pierre Danthine, 1983. "The Time Pattern of Hedging and the Volatility of Futures Prices," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(2), pages 249-266.
    7. Adler, Michael & Detemple, Jerome B, 1988. " On the Optimal Hedge of a Nontraded Cash Position," Journal of Finance, American Finance Association, vol. 43(1), pages 143-153, March.
    8. Ho, Thomas S Y, 1984. "Intertemporal Commodity Futures Hedging and the Production Decision," Journal of Finance, American Finance Association, vol. 39(2), pages 351-376, June.
    9. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
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