This study is an empirical test on the validity of an option pricing model and an efficiency of options market. In order to study these issues, this thesis employes an option pricing model developed by Kim(1992) and examines the relation between implied volatility computed from the data for Primes and Scores and historical volatility. Volatility of excess return which is a difference between rate of return on stock and risk free interest rate plays an important role in option pricing under stochastic interest rate. Beckers (1981) noted that using the Black-Scholes option pricing model, there seems to be reasonable evidence to question the option market efficiency. However, this thesis does not find such evidence. The discrepancy between these results and Becker's can be attributable to volatility of risk free interest rate. It is found that even though Kim's model (1992) improves upon the Black-Sholes option pricing model, it still does not eliminate biases with respect to exercise price.