Option-Implied Risk-Neutral Distributions and Implied Binomial Trees

Abstract

Solving backward through an option pricing model to find the “implied volatility” (IV) that makes the model value equal the market price is a technique nearly as old as the Black-Scholes model itself. In fact, calculating the implied volatility yields the entire implied risk-neutral returns distribution: It is lognormal with mean equal to the riskless interest rate and constant volatility equal to IV. But research across many different options markets has shown clearly that neither implied nor empirical volatility is constant, and returns distributions appear to be far from lognormal. This has led to new theoretical pricing models that can incorporate non-constant volatility and more general returns distributions. It has also led to techniques for obtaining the entire risk-neutral returns distribution implied in a full set of market prices for options with different strikes and maturities. One of the most general and flexible approaches, first suggested by Rubinstein, is to construct an implied binomial tree.This article leads off our Symposium on the topic of implied distributions. In it, Jackwerth presents a comprehensive review of the literature on option-implied risk neutral distributions and implied valuation trees.