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.