Before revision:  As the result we extend a set of the tractable Levy models which represent the jumps as a sum of the idiosyncratic and common parts. So far in the literature only the discrete and exponential jumps were considered using Marshall and Olkin (1967) method , and only in one and two-dimensional cases. We present realization of our approach in two and three dimensional cases, i. e. compute joint survival probabilities Q of two or three counterparties.
After revision:  As the result we extend a set of the tractable Levy models which represent the jumps as a sum of the idiosyncratic and common components. The multi-dimensional problem is made tractable via a novel computational method, which generalizes the one-dimensional fractional partial differential equation method of Itkin, 2014 to the two- and three-dimensional cases. This method is unconditionally stable and of the second order of approximation in space and time; in addition, for many popular Levy models it has linear complexity in each dimension. Marginal and joint survival probabilities Q of two or three counterparties.