Correcting the Bias in the Practitioner Black-Scholes Method

Yin, Yun and Moffatt, Peter (2019) Correcting the Bias in the Practitioner Black-Scholes Method. Journal of Risk and Financial Management, 12 (4). ISSN 1911-8066

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Abstract

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 (see Christoffersen and Jacobs, 2004, p.298) 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 (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 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.

Item Type: Article
Uncontrolled Keywords: option pricing,practitioner black-scholes method,smearing,non-linear least squares,monte carlo
Faculty \ School: Faculty of Social Sciences > School of Economics
Depositing User: LivePure Connector
Date Deposited: 23 Sep 2019 11:30
Last Modified: 25 Jun 2020 00:37
URI: https://ueaeprints.uea.ac.uk/id/eprint/72348
DOI: 10.3390/jrfm12040157

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