The Information Frown in Option Prices

Abstract

It is well known that for options with the same expiration date, levels of implied volatility differ systematically by strike price in a smile or smirk pattern. We show that (in the equity index options market) information content also differs systematically by strike price displaying a pattern. Implied volatilities calculated from near-the-money, and particularly from moderately high strike price, options contain considerable information regarding future volatility and efficiently subsume the information in the historical record. Implied volatilities calculated from far-from-the-money options (particularly options with low strike prices) are much less informative and do not incorporate the information in the asset's price history. While the prices of near-the-money and moderately high strike price options appear largely determined by the market's expectations of future volatility, the prices of far-from-the-money and low-strike-price options appear to be largely determined by factors other than the market's volatility expectation. These other determinants of implied volatility are apparently long-lived or persistent since the frown cannot be attributed to transitory factors. Theories of the smile need to not only explain why volatility levels differ by strike price but should also explain why implied volatilities at some strike prices are largely determined by the market's volatility expectations while others appear relatively independent of these expectations.