Black-Scholes Option Pricing Formula - An empirical study

Abstract

Purpose: The purpose of this study is to empirically test the accuracy of the Black and Scholes model by examining the difference between theoretical prices predicted by the model and actual market prices. We will also try to determine whether the accuracy of the model varies with the time left to expiration or the moneyness of an option. Method: In order to examine the accuracy of the model we will compare the theoretical option prices of the model to the actual prices observed on the market. We will also examine how the differences in price relates to time left to expiration and moneyness, meaning the degree in which the options are in- or out-of-the-money, of the options. The stocks chosen for this study are the five Swedish stocks on the OMX Nordic Exchange whose options had the largest total trading volume during 2007. The stock options in question are ABB, Astra Zeneca, Boliden, Ericsson and Hennes & Mauritz. Conclusion: When conducting the study we found that approximately 70% of all our observed options had less than 90 days to expiration, approximately 60% of all observations were out-of-the-money and the center of gravity for all observations was shifted towards being out-of-the-money and underpriced by the Black and Scholes model. The conclusion of the study is that the relative pricing error is generally larger for observations out-of-the-money than for observations in-the-money. And secondly, the relationship between relative pricing error and time left to expiry suggests that options with little time left to expiry are priced slightly less accurately than options with longer time left to expiry.