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Random Dynamics and Finance: Constructing Implied Binomial Trees from a Predetermined Stationary Den

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  • Wael Bahsoun

    ()
    (University of Victoria)

  • Pawel Góra

    ()
    (Concordia University)

  • Silvia Mayoral

    ()
    (Universidad de Navarra)

  • Manuel Morales

    ()
    (University of Montreal)

Abstract

We introduce a general binomial model for asset prices based on the concept of random maps. The asymptotic stationary distribution for such model is studied using techniques from dynamical systems. In particular, we present a technique to construct a general binomial model with a predetermined stationary distribution. This technique is independent of the chosen distribution making our model potentially useful in financial applications. We brie y explore the suitability of our construction as an implied binomial tree.

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Bibliographic Info

Paper provided by School of Economics and Business Administration, University of Navarra in its series Faculty Working Papers with number 13/06.

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Publication status: Published, Applied Stochastics models in Business and Industry, 2007, vol. 23(3): pp. 181-212.
Handle: RePEc:una:unccee:wp1306

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Web page: http://www.unav.es/facultad/econom

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  1. Klaus Reiner Schenk-Hoppé, . "Random Dynamical Systems in Economics," IEW - Working Papers 067, Institute for Empirical Research in Economics - University of Zurich.
  2. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, American Finance Association, vol. 51(5), pages 1611-32, December.
  3. Tina Hviid Rydberg, 1999. "Generalized Hyperbolic Diffusion Processes with Applications in Finance," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(2), pages 183-201.
  4. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, Elsevier, vol. 7(3), pages 229-263, September.
  5. Jackwerth, Jens Carsten, 1999. "Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review," MPRA Paper 11634, University Library of Munich, Germany.
  6. 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.
  7. Jackwerth, Jens Carsten & Rubinstein, Mark, 2003. "Recovering Probabilities and Risk Aversion from Option Prices and Realized Returns," MPRA Paper 11638, University Library of Munich, Germany, revised 2004.
  8. Constantinides, George M. & Jackwerth, Jens Carsten & Perrakis, Stylianos, 2007. "Option Pricing: Real and Risk-Neutral Distributions," MPRA Paper 11637, University Library of Munich, Germany.
  9. Friedrich Hubalek & Walter Schachermayer, 1998. "When Does Convergence of Asset Price Processes Imply Convergence of Option Prices?," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 8(4), pages 385-403.
  10. Jackwerth, Jens Carsten, 1996. "Generalized Binomial Trees," MPRA Paper 11635, University Library of Munich, Germany, revised 12 May 1997.
  11. He, Hua, 1990. "Convergence from Discrete- to Continuous-Time Contingent Claims Prices," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 523-46.
  12. Francine Diener & MARC Diener, 2004. "Asymptotics of the price oscillations of a European call option in a tree model," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 14(2), pages 271-293.
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