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Utility based pricing of contingent claims

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Author Info

  • A. Gamba

    (Venice University)

  • P. Pellizzari

    (Venice University)

Abstract

In a discrete setting, we develop a model for pricing a contingent claim. Since the presence of hedging opportunities influences the price of a contingent claim, first we introduce the optimal hedging strategy assuming a contingent claim has been issued: a strategy implemented by investing the budget plus the selling price is optimal if it maximizes the expected utility of the agent's revenue, which is the difference between the outcome of the hedging portfolio and the payoff of the claim. Next, we introduce the `reservation price' as a subjective valuation of a contingent claim. This is defined as the minimum price to be added to the initial budget that makes the issue of the claim more preferable than optimally investing in the available securities. We define the reservation price both for a short position (reservation selling price) and for a long position (reservation buying price) in the contingent claim. When the contingent claim is redundant, both the selling and the buying price collapse in the usual Arrow-Debreu price. We develop a numerical procedure to evaluate the reservation price and two applications are provided. Different utility functions are used and some qualitative properties of the reservation price are shown.

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File URL: http://128.118.178.162/eps/fin/papers/9902/9902003.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Finance with number 9902003.

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Length: 30 pages
Date of creation: 08 Feb 1999
Date of revision: 14 Oct 2002
Handle: RePEc:wpa:wuwpfi:9902003

Note: Type of Document - LaTex; prepared on Mac; to print on PostScript; pages: 30; figures: included
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Web page: http://128.118.178.162

Related research

Keywords: Incomplete markets; reservation price; expected utility; optimization;

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References

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  1. Boyle, Phelim P., 1988. "A Lattice Framework for Option Pricing with Two State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(01), pages 1-12, March.
  2. Magill, Michael & Shafer, Wayne, 1991. "Incomplete markets," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 30, pages 1523-1614 Elsevier.
  3. Bernard Bensaid & Jean-Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86.
  4. Duffie, Darrell & Skiadas, Costis, 1994. "Continuous-time security pricing : A utility gradient approach," Journal of Mathematical Economics, Elsevier, vol. 23(2), pages 107-131, March.
  5. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
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Cited by:
  1. L. Boukas & Diogo Pinheiro & Alberto A. Pinto & S. Z. Xanthopoulos & A. N. Yannacopoulos, 2011. "Behavioural and dynamical scenarios for contingent claims valuation in incomplete markets," CEMAPRE Working Papers 1103, Centre for Applied Mathematics and Economics (CEMAPRE), School of Economics and Management (ISEG), Technical University of Lisbon.

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