2014/08/27 by Andrey Itkin, Itkin, Andrey, Alexander Lipton +1
Economics, Econometrics and Finance · #Computational Finance (q-fin.CP) #Credit Risk and Financial Regulations #FOS: Economics and business #Financial Risk and Volatility Modeling #Mathematical Finance (q-fin.MF) #Pricing of Securities (q-fin.PR) #Risk Management (q-fin.RM) #Stochastic processes and financial applications #q-fin.CP #q-fin.MF #q-fin.PR #q-fin.RM
paper · pdf · doi:10.48550/arxiv.1408.6513
43 pages, 18 figures, 8 tables
openalex publication_date 2014/08/27 · arxiv created 2014/11/24 · arxiv updated 2014/11/25 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
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.