| Abstract: | In this paper, the valuation of stock and index options is analyzed in the context of Merton's model of capital market equilibrium with incomplete information. It is possible to derive a partial differential equation for options in such a context. The derivation gives more understanding of the way an option's future payoff is discounted to the present. In order to estimate some of its parameters, the model is calibrated to market prices. It is tested using market prices and the authors' valuation formula. It is found that model prices are not significantly different from market prices, especially when out-of-the-money and deep-in-the-money options are considered. The model gives an explanation to the “strike bias” and the “smile effect.” Simulations of models based respectively on stochastic volatilities and gamma processes, are in accordance with the findings in this paper concerning biases in the Black and Scholes model, especially for pricing deep-in-the-money and out-of-the-money options. Even if the estimation method has its drawbacks, the costs of gathering and processing information regarding the option and its underlying asset play a central role in explaining the biases observed in the Black and Scholes model and help also the understanding of the U-shaped curve known as the smile of volatilities. |
