A Note on Pricing Derivartives in an Incomplete Market

The assumption of the complete market simplifies the whole theory of arbitrage pricing theory since the pioneering work of Black and Scholes. The martingale approach is one of the most powerful tool for pricing derivative securities in the complete market. The existence of such a market, however, may not be guaranteed in the real world, where the martingale mesure is not unique. Therefore, it is more natural to work on the incomplete market. We consider this problem in the simple discrete time and state model. We will present new approach of choosing the martingale measure, which is the combination of the method of least squares and the embedded complete markets.