The theory of option valuation.
Although options have been traded for many centuries, it has remained a relatively thinly traded financial instrument. Paradoxically, the theory of option pricing has been studied extensively. This is due to the fact that many of the financial instruments that are traded in the market place have an option-like structure, and thus the development of a methodology for option-pricing may lead to a general methodology for the pricing of these derivative-assets. This thesis will focus on the development of the theory of option pricing. Initially, a fundamental principle that underlies the theory of option valuation will be given. This will be followed by a discussion of the different types of option pricing models that are prevalent in the literature. Special attention will then be given to a detailed derivation of both the Black-Scholes and the Binomial Option pricing models, which will be followed by a proof of the convergence of the Binomial pricing model to the Black-Scholes model. The Black-Scholes model will be adapted to take into account the payment of dividends, the possibility of a changing inter est rate and the possibility of a stochastic variance for the rate of return on the underlying as set. Several applications of the Black-Scholes model will finally be presented.