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The structural default model of Lipton and Sepp, 2009 is generalized for aset of banks with mutual interbank liabilities whose assets are driven bycorrelated Levy processes with idiosyncratic and common components. Themulti-dimensional problem is made tractable via a novel computational method,which generalizes the one-dimensional fractional partial differential equationmethod of Itkin, 2014 to the two- and three-dimensional cases. This method isunconditionally stable and of the second order of approximation in space andtime; in addition, for many popular Levy models it has linear complexity ineach dimension. Marginal and joint survival probabilities for two and threebanks with mutual liabilities are computed. The effects of mutual liabilitiesare discussed, and numerical examples are given to illustrate these effects.

Efficient solution of structural default models with correlated jumps and mutual obligations