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

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...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 294; pp. 177 - 195
Main Authors: Kim, Jerim, Kim, Bara, Wee, In-Suk
Format: Journal Article
Language:English
Published: Elsevier B.V 01.03.2016
Subjects:
Algorithms
Defaultable bond pricing
Factorization
First passage time
Inversions
Iterative algorithm
Iterative algorithms
Jump–diffusion
Laplace transform
Laplace transforms
Mathematical analysis
Mathematical models
Regime-switching
Switching
65C40
Regime-switching
First passage time
Iterative algorithm
Defaultable bond pricing
60J25
Laplace transform
Jump–diffusion
60J22
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary: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.
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content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2015.08.015