F. Black, “The Pricing of Commodity Contracts,” Journal of Financial Economics, Vol. 3, 1976, pp. 167-179. doi:10.1016/0304-405X(76)90024-6

has been cited by the following article:

• TITLE: Black-Scholes Option Pricing Model Modified to Admit a Miniscule Drift Can Reproduce the Volatility Smile

  AUTHORS: Matthew C. Modisett, James A. Powell

  KEYWORDS: Option Pricing; Black-Scholes; Volatility Smile

  JOURNAL NAME: Applied Mathematics, Vol.3 No.6, June 26, 2012

  ABSTRACT: This paper develops a closed-form solution to an extended Black-Scholes (EBS) pricing formula which admits an implied drift parameter alongside the standard implied volatility. The market volatility smiles for vanilla call options on the S&P 500 index are recreated fitting the best volatility-drift combination in this new EBS. Using a likelihood ratio test, the implied drift parameter is seen to be quite significant in explaining volatility smiles. The implied drift parameter is sufficiently small to be undetectable via historical pricing analysis, suggesting that drift is best considered as an implied parameter rather than a historically-fit one. An overview of option-pricing models is provided as background.