A de-singularized meshfree approach to default probability estimation under a regime-switching synchronous-jump tempered stable Lévy model. (May 2023)

• Record Type: Journal Article
• Authors: Damircheli, Davood; Razzaghi, Mohsen; Kazemi, Seyed-Mohammad-Mahdi; Bastani, Ali Foroush
• Is Part Of: Engineering analysis with boundary elements. Volume 150(2023)
• Page Start: 364
• Page End: 373
• Publication Date: 2023-05
• Subjects: Default probability -- Structural credit risk model -- Strictly positive-definite functions -- Radial basis function collocation -- Regime switching -- Tempered stable Lévy process; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2023.01.033
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: The default probability of a publicly-traded company is modeled by a synchronous-jump regime-switching model in the paper (Hainaut and Colwell, 2016). In this investigation, we first generalize the proposed Lévy model to a more general setting of tempered stable processes recently introduced into the finance literature. However, the resulting integro-partial differential operator suffers from a singularity, thus a general framework based on strictly positive-definite functions is proposed as a remedy 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 prove that considering some regularity assumptions, the proposed method automatically de-singularizes the problem in the tempered stable case. Finally, we perform some numerical experiments using the proposed method on some standard examples from the literature which confirm the validity of our theoretical results and the stability of the numerical algorithm.