Some Remarks on Two - Asset Options Pricing and Stochastic Dependence of Asset Prices

In this short note, we consider some problems of two - asset options pricing. In particular, we investigate the relationship between options prices and the 'correlation' parameter in the Black - Scholes model. Then, we consider the general case in the framework of the copula construction of risk - neutral distributions. This extension involves results on the supermodular order applied to the Feynman - Kac representation. We show that it could be viewed as a generalization of a maximum principle for parabolic PDE