Next Article in Journal
Are CDS Spreads Sensitive to the Term Structure of the Yield Curve? A Sector-Wise Analysis under Various Market Conditions
Next Article in Special Issue
Testing the Information-Based Trading Hypothesis in the Option Market: Evidence from Share Repurchases
Previous Article in Journal
Dynamic Responses of Major Equity Markets to the US Fear Index
Previous Article in Special Issue
Volatility Integration in Spot, Futures and Options Markets: A Regulatory Perspective
Open AccessArticle

Correcting the Bias in the Practitioner Black-Scholes Method

by 1 and 2,*
School of Business, Macau University of Science and Technology, Avenida Wai Long, Taipa, Macau
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;
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
Show Figures

Figure 1

MDPI and ACS Style

Yin, Y.; Moffatt, P.G. Correcting the Bias in the Practitioner Black-Scholes Method. J. Risk Financial Manag. 2019, 12, 157.

AMA Style

Yin Y, Moffatt PG. Correcting the Bias in the Practitioner Black-Scholes Method. Journal of Risk and Financial Management. 2019; 12(4):157.

Chicago/Turabian Style

Yin, Yun; Moffatt, Peter G. 2019. "Correcting the Bias in the Practitioner Black-Scholes Method" J. Risk Financial Manag. 12, no. 4: 157.

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

Search more from Scilit
Back to TopTop