Abstract
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.
| Original language | English |
|---|---|
| Article number | 10268 |
| Pages (from-to) | 177-195 |
| Number of pages | 19 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 294 |
| DOIs | |
| Publication status | Published - 2016 Mar 1 |
Bibliographical note
Funding Information:We are grateful to the referees for their many valuable comments and suggestions which significantly improved this article. B. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIP) (No. 2014R1A2A2A01005831 ).
Publisher Copyright:
© 2015 Elsevier B.V.
Keywords
- Defaultable bond pricing
- First passage time
- Iterative algorithm
- Jump-diffusion
- Laplace transform
- Regime-switching
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics