An implied volatility index from stock options : construction and properties

Abstract

A widely studied and quite useful measure of volatility is the implied volatility index. Although, there is a growing literature on the construction and the properties of implied volatility indices (Fleming et al., 1995, Whaley, 1993, and 2000, Wagner and Szimayer, 2000), to the best of our knowledge there has not yet been constructed and examined an implied volatility index on an individual stock. And this is the purpose of this paper. By construction, Implied Volatility Indices are weighted averages of the implied volatilities computed from call and puts near-the-money, nearby and second nearby option contracts on the relevant underlying stock index and they represent the implied volatility of a synthetic option that has constant time to maturity (usually 22 trading days) and fixed strike price (usually at-the-money). In this paper, we construct an implied volatility index on the General Motors U.S. stock (GM), with the methodology of VIX (CBOE VIX white paper, 2003), we call it GMVIX, and then we try to investigate its properties. We are confident that this study will contribute significantly in the relative literature and will be of interest to practitioners as well.