The Black-Scholes model and the pricing of stock options in South Africa

Master Thesis


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University of Cape Town

Option Pricing Theory (OPT), along with the Capital Asset Pricing Model, the Theory of Capital Structure, and the Efficient Markets Hypothesis, form one of the pillars of modem finance theory. Central to OPT is the Black-Scholes model, the first option pricing model derived within a general equilibrium framework, and therefore consistent with all arbitrage conditions an asset pricing model must satisfy. An attempt is made at explaining this model, and the first part of the paper is devoted to this objective. The appreciation of the theoretical elegance of the Black-Scholes model can be considerably enhanced through the understanding of the issues that made (and still make in the case of American put options) the derivation of an equilibrium model of option pricing such an immense task. With the intention of emphasising such issues, the first section of Part One covers the option pricing models that had been suggested before Black and Scholes (and Merton). This helps to put the Black-Scholes model in context, as well as facilitate an understanding of the approach Black and Scholes adopted in developing their model. Its derivation is the central focus of section 3, the second section of Part One. The second part of the paper contains an attempt at testing the Black-Scholes model, first in its "pure form," and then adjusted to account for the possibility of early exercise. Simple regression tests are performed, where daily prices of a sample of stock options traded on the Johannesburg Stock Exchange are used as dependent variables in regression equations. Black-Scholes model prices are computed, and used as the explanatory variables in these equations. But before the tests could be conducted, the distributions of the underlying assets' returns had to be examined and due consideration had to be given to the estimation of the volatility parameters. Part Two starts with a very brief overview of the South African exchange-traded stock options market. This is followed by a description of the data used in the tests, and discussions on the statistical behaviour of the underlying assets. A discussion on volatility estimating follows, and the test results are then presented.

Bibliography: leaves 52-54.