THREE ESSAYS IN THE USE OF OPTION PRICING THEORY (COX, ROSS, RUBINSTEIN, BLACK-SCHOLES)

The first essay presents an extension of the Cox-Ross-Rubinstein simplified approach to Option pricing. In this approach, a discrete time binomial model is used to value an option on a single asset by arbitrage considerations. By taking this model to the limit in the appropriate way, the well known continuous time models (eg. Black-Scholes) may be elegantly derived. This essay shows how to extend the binomial approach to the case of multiple stochastic process. It is shown how this technique may be used to value options on a portfolio, stock options in the presence of stochastic interest rates, etc. Finally, some insight into the technique is gained by demonstrating the results of erroneous application of the method.;In the third essay, a linear multiple factor risk model for stock option returns is presented. Option excess return is linked to the excess return on the underlying stock, and to other factors which account for the non-equity like behavior of options. Linearity is achieved by taking a Taylor expansion of the Black-Scholes formula to model month end option values. Certain empirical adjustments are then introduced to correct for some of the defects in Black-Scholes. The performance of the model is examined over the period 1978 through 1982. Finally, some examples of portfolio risk analysis are presented, showing how the model may be used to compute portfolio risk and beta.;The second essay contains an empirical investigation of Rubinstein's Displaced Diffusion option pricing model. This model is an extension of the Black-Scholes model, in which the underlying source of risk if pushed back to the assets of the firm, with the common stock regarded as a derivative asset. The analysis is done by comparison with the Black-Scholes model. Using the Berkeley Options Data Base, the stochastic processes of eighteen stocks are fitted by maximum likelihood methods for each model. In addition, parameter values for each model are implied independently from option prices, and compared for goodness of fit. The results show that with careful parameter estimation, the Displaced Diffusion model has the ability to explain the historical behavior of both stock and option prices consistently better than Black-Scholes.