  Pricing of high-dimensional options is a deep problem of the Theoretical
Financial Mathematics. In this article we present a new class of L\'{e}vy
driven models of stock markets. In our opinion, any market model should be
based on a transparent and intuitively easily acceptable concept. In our case
this is a linear system of stochastic equations. Our market model is based on
the principle of inheritance, i.e. for the particular choice of parameters it
coincides with known models. Also, the model proposed is effectively
numerically realizable. For the class of models under cosideration, we give an
explicit representations of characteristic functions. This allows us us to
construct a sequence of approximation formulas to price basket options. We show
that our approximation formulas have almost optimal rate of convergence in the
sense of respective n-widths.
