  The structural default model of Lipton and Sepp, 2009 is generalized for a
set of banks with mutual interbank liabilities whose assets are driven by
correlated Levy processes with 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 for two and three
banks with mutual liabilities are computed. The effects of mutual liabilities
are discussed, and numerical examples are given to illustrate these effects.
