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Arbitrage pricing and equilibrium pricing : compatibility conditions

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  • Elyès Jouini

    ()
    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX)

  • Clotilde Napp

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX)

Abstract

The problem of fair pricing of contingent claims is well understood in the contex of an arbitrage free, complete financial market, with perfect information : the so-called arbitrage approach permits to construct a unique valuation operator compatible with observed price processes. In the more realistic context of partial information, the equilibrium analysis permits to construct a unique valuation operator which only depends on some particular price processes as well as on the dividends process. In this paper we present these two approaches and we explore their links and the conditions under which they are compatible ; In particular, we derive from the equilibrium conditions some links between the price processes paramaters and those of the dividend processes paramaters

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Bibliographic Info

Paper provided by HAL in its series Post-Print with number halshs-00176423.

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Date of creation: 2002
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Publication status: Published, Collected Papers of the New York University Mathematical Finance Seminar, New York University (Ed.), 2002, 131-159
Handle: RePEc:hal:journl:halshs-00176423

Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00176423/en/
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Related research

Keywords: Arbitrage; equilibrium; optimality; incomplete markets; nonredudant assets; derivatives pricing;

References

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  1. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
  2. Bick, Avi, 1990. " On Viable Diffusion Price Processes of the Market Portfolio," Journal of Finance, American Finance Association, vol. 45(2), pages 673-89, June.
  3. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
  4. Elyès Jouini & Vincent Porte, 2007. "Efficient Trading Strategies," Working Papers halshs-00176616, HAL.
  5. Elyès Jouini & Hédi Kallal, 1997. "Viability and Equilibrium in Securities Markets with Frictions," Working Papers 97-07, Centre de Recherche en Economie et Statistique.
  6. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
  7. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
  8. Bick, Avi, 1987. "On the Consistency of the Black-Scholes Model with a General Equilibrium Framework," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(03), pages 259-275, September.
  9. He, Hua & Leland, Hayne, 1993. "On Equilibrium Asset Price Processes," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 593-617.
  10. Elyès Jouini & Clotilde Napp, 1998. "Contiuous Time Equilibrium Pricing of Nonredundant Assets," Working Papers 98-30, Centre de Recherche en Economie et Statistique.
  11. 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.
  12. Duffie, Darrell & Zame, William, 1989. "The Consumption-Based Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 57(6), pages 1279-97, November.
  13. Araujo, A. & Monteiro, P. K., 1989. "Equilibrium without uniform conditions," Journal of Economic Theory, Elsevier, vol. 48(2), pages 416-427, August.
  14. Araujo,A. & Monteiro,P.K., 1989. "General equilibrium with infinitely many goods: The case of seperable utilities," Discussion Paper Serie A 249, University of Bonn, Germany.
  15. Huyěn Pham & Nizar Touzi, 1996. "Equilibrium State Prices In A Stochastic Volatility Model," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 215-236.
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