Abstract
We address a number of technical problems with the popular Practitioner BlackScholes (PBS) method for valuing options. The method amounts to a twostage procedure in which fitted values of implied volatilities (IV) from a linear regression are plugged into the BlackScholes formula to obtain predicted option prices. Firstly we ensure that the prediction from stage one is positive by using loglinear regression. Secondly, we correct the bias (see Christoffersen and Jacobs, 2004, p.298) that results from the transformation applied to the fitted values (i.e. the BlackScholes formula) being a highly nonlinear function of implied volatility. We apply the smearing technique (Duan, 1983) 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 nonlinear 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 insample and outofsample; (2) using standard (loglinear) 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, loglinear PBS with smearing is preferred on the basis that it is the only approach that results in valuations with negligible bias.
Original language  English 

Article number  157 
Journal  Journal of Risk and Financial Management 
Volume  12 
Issue number  4 
DOIs  
Publication status  Published  26 Sep 2019 
Keywords
 Option pricing
 Practitioner BlackScholes method
 Smearing
 Nonlinear least squares
 Monte Carlo
Profiles

Peter Moffatt
 School of Economics  Professor of Econometrics
 Norwich Institute for Healthy Aging  Member
 Centre for Behavioural and Experimental Social Science  Member
 Applied Econometrics And Finance  Member
 Behavioural Economics  Member
Person: Research Group Member, Research Centre Member, Academic, Teaching & Research