| Implied volatility provides information which is useful for not only investors, but farmers, producers, manufacturers and corporations. These market participants use implied volatility as a measure of price risk for hedging and speculation decisions. Because volatility is a constantly changing variable, there needs to be a simple and quick way to extract its value from the Black-Scholes model. Unfortunately, there is no closed form solution for the extraction of the implied volatility variable; therefore its value must be approximated. This study investigated the relative accuracy of six methods for approximating Black-Scholes implied volatility developed by Curtis and Carriker, Brenner and Subrahmanyam, Chargoy-Corona and Ibarra-Valdez, Bharadia et al., Li (2005) and Corrado and Miller. Each of these methods were tested and analyzed for accuracy using nearest to the money options over two data sets, corn and live cattle, spanning contract years 1989 to 2008 and 1986 to 2008, respectively. This study focuses on accuracy for nearest-to-the-money options because the majority of traded options are concentrated at or near-the-money and several of the approximations were developed for at-the-money options.;Rather than following only the traditional measures of testing approximations for accuracy, this study considered several alternative ways for testing accuracy. In addition to analyzing mean errors and mean percent errors, other moments of the error distributions such as variance and skewness were analyzed. Beyond this, measures of goodness of fit, determined through an adjusted R2, and accuracy over observed changes in market variables, such as moneyness, time to maturity and interest rates, were analyzed.;The results were divided into three distinct groups, with the first group comprised of only the Corrado and Miller approximation. This method was clearly the most accurate, followed by Bharadia et al. and Li (2005) in the second group and finally the Curtis and Carriker, Brenner and Subrahmanyam, Chargoy-Corona and Ibarra-Valdez methods in the third group. |
