Implied Binomial Trees

  • Author(s): MARK RUBINSTEIN
  • Published: Apr 30, 2012
  • Pages: 771-818
  • DOI: 10.1111/j.1540-6261.1994.tb00079.x


This article develops a new method for inferring risk‐neutral probabilities (or state‐contingent prices) from the simultaneously observed prices of European options. These probabilities are then used to infer a unique fully specified recombining binomial tree that is consistent with these probabilities (and, hence, consistent with all the observed option prices). A simple backwards recursive procedure solves for the entire tree. From the standpoint of the standard binomial option pricing model, which implies a limiting risk‐neutral lognormal distribution for the underlying asset, the approach here provides the natural (and probably the simplest) way to generalize to arbitrary ending risk‐neutral probability distributions.

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