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

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Author Info
Wael Bahsoun () (University of Victoria)
Pawel Góra () (Concordia University)
Silvia Mayoral () (Universidad de Navarra)
Manuel Morales () (University of Montreal)

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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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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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  1. 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. [Downloadable!]
  2. Jens Carsten Jackwerth, 1998. "Generalized Binomial Trees," Finance 9803004, EconWPA. [Downloadable!]
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  3. He, Hua, 1990. "Convergence from Discrete- to Continuous-Time Contingent Claims Prices," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 3(4), pages 523-46. [Downloadable!] (restricted)
  4. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September. [Downloadable!] (restricted)
  5. Francine Diener & MARC Diener, 2004. "Asymptotics of the price oscillations of a European call option in a tree model," Mathematical Finance, Blackwell Publishing, vol. 14(2), pages 271-293. [Downloadable!] (restricted)
  6. Klaus Reiner Schenk-Hoppé, . "Random Dynamical Systems in Economics," IEW - Working Papers iewwp067, Institute for Empirical Research in Economics - IEW. [Downloadable!]
  7. Yacine Aït-Sahalia & Andrew W. Lo, 1998. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," Journal of Finance, American Finance Association, vol. 53(2), pages 499-547, 04. [Downloadable!] (restricted)
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  8. Jens Carsten Jackwerth & George M. Constantinaides & Stylianos Perrakis, 2005. "Option Pricing: Real and Risk-Neutral Distributions," CoFE Discussion Paper 05-06, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
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  9. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-32, December. [Downloadable!] (restricted)
  10. Hua He., 1990. "Convergence from Discrete to Continuous Time Contingent Claims Prices," Research Program in Finance Working Papers RPF-199, University of California at Berkeley.
  11. Jackwerth, Jens Carsten, 1999. "Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review," MPRA Paper 11634, University Library of Munich, Germany. [Downloadable!]
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