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

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DOI: 10.4236/am.2012.36093    4,991 Downloads   7,826 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

M. Modisett and J. Powell, "Black-Scholes Option Pricing Model Modified to Admit a Miniscule Drift Can Reproduce the Volatility Smile," Applied Mathematics, Vol. 3 No. 6, 2012, pp. 597-605. doi: 10.4236/am.2012.36093.

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