具有相关跳和相互义务的结构违约模型的有效解
Efficient solution of structural default models with correlated jumps and mutual obligations
摘要：
Lipton and Sepp，2009的结构性违约模型被推广到一组具有相互银行间负债的银行，其资产由具有特殊成分和共同成分的相关Levy过程驱动。通过一种新的计算方法使多维问题变得易于处理，该方法将Itkin，2014的一维分数偏微分方程方法推广到二维和三维情况。这种方法是无条件稳定的，在空间和时间上具有二阶近似;此外，对于许多流行的Levy模型，它在每个维度上都具有线性复杂性。边际和联合生存概率的两个和三个银行的相互负债计算。讨论了相互负债的影响，并给出了数值例子来说明这些影响。
英文摘要：
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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