Why are Those Options Smiling?

Abstract

The “volatility smile” is a well-known feature of all options markets—well-known, but not well understood, despite the fact that its presence has been documented for many years, and the fact that it represents a really annoying contradiction of our cherished Black-Scholes valuation framework. An enormous amount of research and theoretical modeling have been driven by the desire to “explain” the smile, where “explain” implies finding properties of real-world returns distributions and options markets (fat tails, stochastic volatility, jumps, transactions costs, etc.) such that if the particular deviation from Black-Scholes assumptions were taken properly into account in the valuation model, the apparent smile would disappear. That is, the smile is felt to be caused by the use of the “wrong” pricing model to compute implied volatilities, and under the “true” model, all options would have the same implied volatility (IV). In this article, Ederington and Guan develop strong evidence that that belief is incorrect, without having to specify what the “true” model is. They compute IVs for S&P 500 index futures options from the basic Black 1976 model. If the resulting smile pattern is actually spurious, then a trading strategy of buying low IV contracts and writing high IV contracts should not produce excess returns. But they find that it does. This implies that high IV options really are significantly overpriced relative to low IV options, even though the model used to calculate IV may not be the true model. Exploring their results, they conclude that part of the Black-Scholes smile is spurious, but a substantial part appears to be true mispricing.