Black-Scholes Option Pricing Model Modified to Admit a Miniscule Drift Can Reproduce the Volatility Smile
Black-Scholes Option Pricing Model Modified to Admit a Miniscule Drift Can Reproduce the Volatility Smile作者机构：Department of Mathematics and Statistics Utah State University Logan USA Financial Guard Ltd. London UK
出 版 物：《Applied Mathematics》 (应用数学（英文）)
年 卷 期：2012年第3卷第6期
页 面：597-605页
学科分类：0202[经济学-应用经济学] 02[经济学]
主 题：Option Pricing Black-Scholes Volatility Smile
摘 要：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.
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