How Useful are Implied Distributions?

Abstract

From a set for options with different exercise prices and the same maturity, one can obtain an entire implied risk-neutral probability density for a future date. But the process also impounds pricing “noise” from a variety of sources and the resulting density tends to be too irregular in practice to be entirely plausible. One solution is to restrict the form of the implied distribution to a mixture of known distributions. In this article, the authors constrain the implied distribution from FTSE-100 index options to a combination of two lognormals. This gives a smooth function with a substantially closer fit to market prices than a single lognormal. They then examine option pricing around four market “crash” events and three national elections, in order to assess whether and how implied volatilities in the stock index options market reflect evolving market expectations during these periods of heightened uncertainty. They find that implied distributions seem not to anticipate crashes, but to change immediately afterward. Elections provide more evidence that the market can forecast the election outcome accurately.