MANAGING DERIVATIVES IN THE PRESENCE OF A SMILE EFFECT AND INCOMPLETE INFORMATION

AbstractThis chapter develops a simple option pricing model when markets can make sudden jumps in the presence of incomplete information. Incomplete information can be defined in the context of Merton's (1987) model of capital market equilibrium with incomplete information. In this context, analytic formulas can be derived for options using the Black–Scholes (1973) approach as in Bellalah (1999). The option value depends upon the probability and magnitude of jumps and a continuous volatility. The model is useful in explaining the smile effect and in extracting information costs. The model can be applied to hedging strategies for different strike prices and can be used for the valuation of different types of options. It can also be used in the identification of mispriced options. Some simulations are run with and without shadow costs of incomplete information. We run some simulations to extract information costs using market data. Our model can be used to estimate information costs in different markets.