Option-Implied Risk-Neutral Distributions and Implied Binomial Trees

Determining and benchmarking risk neutral distributions implied from option prices

Implied Binomial Trees

Despite its success, the Black-Scholes formula has become increasingly unreliable over time in the very markets where one would expect it to be most accurate. In addition, attempts by financial economists to extract probabilistic information from option prices have been puny in comparison to what is clearly possible. This paper develops a new method for inferring risk-neutral probabilities (or ...

Valuing Real Options using Implied Binomial Trees

A real option on a commodity is valued using an implied binomial tree (IBT) calibrated using commodity futures options prices. Estimating an IBT in the absence of spot options (the norm for commodities) allows real option models to be calibrated for the first time to market-implied probability distributions for commodity prices. Also, the existence of long-dated futures options means that good ...

An Efficient Implementation of Implied Binomial Trees

Implied binomial trees are constructed by fitting a risk-neutral density (in the form of ending nodal probabilities) to observed option prices. Since there are usually not enough options traded in the marketplace, a quadratic program is often used to extract the ending nodal probabilities from observed option prices. A problem with this commonly used approach is that the quadratic program is us...

Implied Binomial Trees from the Historical Distribution

* We are grateful for helpful comments from Salih Neftci. The comments of an anonymous referee were enormously beneficial. We are grateful for support from the Schweger Fund. Remaining errors are our own.