2021/09/10 by Davood Damircheli, Mohsen Razzaghi, Damircheli, Davood +6
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #Credit Risk and Financial Regulations #FOS: Mathematics #Numerical Analysis (math.NA) #Stochastic processes and financial applications #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.2109.04676
openalex publication_date 2021/09/10 · arxiv created 2021/12/13 · arxiv updated 2021/12/14 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In the paper [Hainaut, D. and Colwell, D.B., \rm A structural model for credit risk with switching processes and synchronous jumps, The European Journal of Finance 22(11) (2016): 1040-1062], the authors exploit a synchronous-jump regime-switching model to compute the default probability of a publicly traded company. Here, we first generalize the proposed Lévy model to more general setting of tempered stable processes recently introduced into the finance literature. Based on the singularity of the resulting partial integro-differential operator, we propose a general framework based on strictly positive-definite functions to de-singularize the operator. We then analyze an efficient meshfree collocation method based on radial basis functions to approximate the solution of the corresponding system of partial integro-differential equations arising from the structural credit risk model. We show that under some regularity assumptions, our proposed method naturally de-sinularizes the problem in the tempered stable case. Numerical results of applying the method on some standard examples from the literature confirms the accuracy of our theoretical results and numerical algorithm.