This thesis explores the biases of the Black and Scholes option pricing model through the comparison between the Black and Scholes model and the compound option pricing model. The historical KOSPI200 index option data from Aug. 1997 to Sep, 2001 have been used. Compound option model, which necessitates the seven variables to derive the theoretical option price is the main tool to deal with the price bias shown by Black and Scholes option model in this paper. Merton model is used for the value of firm debt and the iterative method is also used for the volatility of the firm value, which reaches the optimal solution with a recursive execution.
The result of empirical research shows that the price bias from Black and Scholes option pricing model, that is, out of the money bias and time to expiration bias can well be explained by Compound option model, which contains the leverage effect. The leverage effect implied in the compound option model takes the form of the volatility increase in the decline of stock price and of the volatility decrease in the advance of stock price.
