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Equilibrium Pricing in Incomplete Markets

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  • Elyès Jouini
  • Abdelhamid Bizid

Abstract

Given exogenously the price process of some assets, we constrain the price process of other assets, which are characterized by their final pay-offs. We deal with an incomplete market framework in a discrete time model and assume the existence of the equilibrium. In this setup, we derive restrictions on the state-price deflators and these restrictions do not depend on a particular choice of utility function. A stochastic volatility model is numerically investigated as an example. Our approach leads to an interval of admissible prices much better than the arbitrage pricing interval.

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Bibliographic Info

Paper provided by EconWPA in its series Finance with number 0312004.

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Length: 25 pages
Date of creation: 08 Dec 2003
Date of revision:
Handle: RePEc:wpa:wuwpfi:0312004

Note: Type of Document - pdf; prepared on Win98; pages: 25
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Web page: http://128.118.178.162

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Keywords: equilibrium pricing; incomplete markets; state-price deflator; arbitrage pricing; stochastic volatility;

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References

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  1. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
  2. Dybvig, Philip H, 1988. "Distributional Analysis of Portfolio Choice," The Journal of Business, University of Chicago Press, vol. 61(3), pages 369-93, July.
  3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  4. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  5. Darrell Duffie & William Zame, 1988. "The Consumption-Based Capital Asset Pricing Model," Discussion Papers 88-10, University of Copenhagen. Department of Economics.
  6. Elyes Jouini & Pierre-Francois Koehl, . "Pricing of Non-redundant Derivatives in a Complete Market," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-009, New York University, Leonard N. Stern School of Business-.
  7. Philip H. Dybvig, 1987. "Inefficient Dynamic Portfolio Strategies or How to Throw Away a Million Dollars in the Stock Market," Cowles Foundation Discussion Papers 826R, Cowles Foundation for Research in Economics, Yale University, revised Jan 1988.
  8. Jouini, Elyès & Bizid, Abdelhamid & Koehl, Pierre-François, 1999. "Pricing of non-redundant derivatives in a complete market," Economics Papers from University Paris Dauphine 123456789/5605, Paris Dauphine University.
  9. Perrakis, Stylianos & Ryan, Peter J, 1984. " Option Pricing Bounds in Discrete Time," Journal of Finance, American Finance Association, vol. 39(2), pages 519-25, June.
  10. Elyès Jouini & Hédi Kallal, 1999. "Efficient Trading Strategies in the Presence of Market Frictions," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-035, New York University, Leonard N. Stern School of Business-.
  11. Elyès Jouini & Clotilde Napp, 1998. "Contiuous Time Equilibrium Pricing of Nonredundant Assets," Working Papers 98-30, Centre de Recherche en Economie et Statistique.
  12. Yacine Aït-Sahalia & Andrew W. Lo, . "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," CRSP working papers 332, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
  13. Detemple, Jerome B & Selden, Larry, 1991. "A General Equilibrium Analysis of Option and Stock Market Interactions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(2), pages 279-303, May.
  14. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
  15. Breeden, Douglas T & Gibbons, Michael R & Litzenberger, Robert H, 1989. " Empirical Tests of the Consumption-Oriented CAPM," Journal of Finance, American Finance Association, vol. 44(2), pages 231-62, June.
  16. Ritchken, Peter H, 1985. " On Option Pricing Bounds," Journal of Finance, American Finance Association, vol. 40(4), pages 1219-33, September.
  17. Douglas T. Breeden & Michael R Gibbons & Robert H. Litzenberger, . "Empirical Tests of the Consumption-Oriented CAPM," Rodney L. White Center for Financial Research Working Papers 7-89, Wharton School Rodney L. White Center for Financial Research.
  18. Zhou, Chunsheng, 1999. "Informational Asymmetry and Market Imperfections: Another Solution to the Equity Premium Puzzle," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(04), pages 445-464, December.
  19. Perrakis, Stylianos, 1986. "Option Bounds in Discrete Time: Extensions and the Pricing of the American Put," The Journal of Business, University of Chicago Press, vol. 59(1), pages 119-41, January.
  20. Douglas T. Breeden & Michael R Gibbons & Robert H. Litzenberger, . "Empirical Tests of the Consumption-Oriented CAPM," Rodney L. White Center for Financial Research Working Papers 07-89, Wharton School Rodney L. White Center for Financial Research.
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