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

The structural default model of Lipton and Sepp [Credit value adjustment for credit default swaps via the structural default model, J. Credit Risk 5(2) (2009), pp. 123–146] is generalized for a set of banks with mutual interbank liabilities whose assets are driven by correlated Lévy 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 [Efficient solution of backward jump-diffusion PIDEs with splitting and matrix exponentials, J. Comput. Financ. (2014), forthcoming. Available at http://arxiv.org/abs/1304.3159] 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 Lévy 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.

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