There are two main approaches for pricing the options. The first one is the arbitrage argument of Black and Scholes (1973), and the second one is the equilibrium approach of Cox and Ross (1976). The purpose of this study is to compare and contrast the arbitrage and equilibrium models, to develop a method to estimate the implied market price of risk and to statistically test the consistency of arbitrage and equilibrium models. In the first section of the thesis, we theoretically compare and contrast the arbitrage and equilibrium models and also perform an empirical analysis to show the options pricing results they produce. A method to calculate the implied market price of risk is developed using convergence algorithm. The actual calculation of the implied market price of risk is unique to this study in that although conceptually it has been widely used in theory, its calculation was not found in a literature search. In addition, without an actual calculation of the market price of risk, it is impossible, in practice, to compare the equilibrium and arbitrage models. (Abstract shortened by UMI.)