Financial Market with Interacting Assets. Pricing Barrier Options

A new model of a financial market with several interacting assets is introduced and developed. The mutual interaction of asset prices is described by a general multidimensional linear stochastic differential equation with multiplicative noise. The non-arbitrage and completeness conditions for the model are studied in detail. As an application, the pricing of the outside barrier options and of the floating barrier options based on a 2-dimensional version of the model is considered.