A Test of the Black and Scholes Model of Option Valuation in Australia

Abstract

A model to explain option prices has been developed by Black and Scholes. The approach adopted here is to solve the Black and Scholes equation in reverse to obtain implied variance rates of return on the underlying stocks. These are then converted to a standard deviation basis and compared to various measures of historical standard deviation available at the time of trade and with the standard deviations which actually resulted after that date. It is shown that the model produces biassed estimates and that part of this bias might be explained by incorrect pricing possibly due to a lack of experience with exchange-traded options in Australia. It is shown that the bias has decreased substantially, indicating that a learning process may have occurred in the market.