Iterative algorithm for the first passage time distribution in a jump–diffusion model with regime-switching, and its applications

Jerim Kim ^[1] ; Bara Kim ^[2] ; In-Suk Wee ^[2]
1. [1] Yong In University
  
  Yong In University
  
  Corea del Sur
2. [2] Korea University
  
  Korea University
  
  Corea del Sur
Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 294, Nº 1 (1 March 2016), 2016, págs. 177-195
Idioma: inglés
DOI: 10.1016/j.cam.2015.08.015
Enlaces
- Texto completo
Resumen
- For a regime-switching model with a finite number of regimes and double phase-type jumps, Jiang and Pistorius (2008) derived matrix equations with real parameters for the Wiener–Hopf factorization. The Laplace transform of the first passage time distribution is expressed in terms of the solution of the matrix equations. In this paper we provide an iterative algorithm for solving the matrix equations of Jiang and Pistorius (2008) with complex parameters. This makes it possible to obtain numeric values of the Laplace transform with complex parameters for the first passage time distribution. The Laplace transform with complex parameters can be inverted by numerical inversion algorithms such as the Euler method. As an application, we compute the prices of defaultable bonds under a structural model with regime switching and double phase-type jumps.