Nonparametric tests of strike price and expiration bias in the implied volatility of the South African All Share Index Future Contract

Abstract

In this article we assess the appropriateness of the constant volatility assumption required by the Black (1976) option pricing model for options on the All Share Index future. The assessment uses similar nonparametric tests as implemented in Rubinstein for data recorded over the 1992 to 1996 period. In the nonparametric tests we focus on the examination of constant volatility across both striking prices as well as expiration dates. The nonparametric tests are not only based on traditional measures of statistical significance to examine the constant volatility assumption, but also utilize a measure of economic importance to assess the practical usefulness of the results. Our empirical results of both measures suggest that the assumption of constant volatility is inappropriate for options on the All Share Index future. Our results point to a pattern of rising volatility with increasing time to expiration and a higher volatility for out-of-the-money options compared to at-the-money options. This evidence is consistent with evidence in international markets found in the USA and the Netherlands.