## The theory of option valuation.

##### Abstract

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.