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Open AccessArticle

Correcting the Bias in the Practitioner Black-Scholes Method

by Yun Yin 1 and Peter G. Moffatt 2,*
1
School of Business, Macau University of Science and Technology, Avenida Wai Long, Taipa, Macau
2
School of Economics, University of East Anglia, Norwich Research Park, Norwich, Norfolk NR4 7TJ, UK
*
Author to whom correspondence should be addressed.
J. Risk Financial Manag. 2019, 12(4), 157; https://doi.org/10.3390/jrfm12040157
Received: 16 August 2019 / Revised: 20 September 2019 / Accepted: 23 September 2019 / Published: 26 September 2019
(This article belongs to the Special Issue Option Pricing)
We address a number of technical problems with the popular Practitioner Black-Scholes (PBS) method for valuing options. The method amounts to a two-stage procedure in which fitted values of implied volatilities (IV) from a linear regression are plugged into the Black-Scholes formula to obtain predicted option prices. Firstly we ensure that the prediction from stage one is positive by using log-linear regression. Secondly, we correct the bias that results from the transformation applied to the fitted values (i.e., the Black-Scholes formula) being a highly non-linear function of implied volatility. We apply the smearing technique in order to correct this bias. An alternative means of implementing the PBS approach is to use the market option price as the dependent variable and estimate the parameters of the IV equation by the method of non-linear least squares (NLLS). A problem we identify with this method is one of model incoherency: the IV equation that is estimated does not correspond to the set of option prices used to estimate it. We use the Monte Carlo method to verify that (1) standard PBS gives biased option values, both in-sample and out-of-sample; (2) using standard (log-linear) PBS with smearing almost completely eliminates the bias; (3) NLLS gives biased option values, but the bias is less severe than with standard PBS. We are led to conclude that, of the range of possible approaches to implementing PBS, log-linear PBS with smearing is preferred on the basis that it is the only approach that results in valuations with negligible bias. View Full-Text
Keywords: option pricing; Practitioner Black-Scholes method; smearing; non-linear least squares; Monte Carlo option pricing; Practitioner Black-Scholes method; smearing; non-linear least squares; Monte Carlo
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Yin, Y.; Moffatt, P.G. Correcting the Bias in the Practitioner Black-Scholes Method. J. Risk Financial Manag. 2019, 12, 157.

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