Using a structural default model considered in Lipton and Sepp ( 2009 ) we propose a new approach to introducing correlated jumps into this framework. 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. We also extend the model by taking into account mutual liabilities of the counterparties and demonstrate their influence on Q. The latter, however, requires a more detailed analysis which will be published elsewhere .
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 .
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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
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
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Q of two or three counterparties. We also extend the model by taking into account mutual liabilities of the counterparties and demonstrate their influence on Q. The latter, however, requires a more detailed analysis which will be published elsewhere
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