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

Jerim Kim, Bara Kim, In-Suk Wee

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Article number10268
Pages (from-to)177-195
Number of pages19
JournalJournal of Computational and Applied Mathematics
Volume294
DOIs
Publication statusPublished - 2016 Mar 1

Fingerprint

Jump-diffusion Model
Regime Switching
First Passage Time
Laplace transforms
Iterative Algorithm
Matrix Equation
Laplace transform
Jump
Wiener-Hopf Factorization
Regime-switching Model
Factorization
Numerical Inversion
Euler's method
Structural Model
Numerics

Keywords

  • Defaultable bond pricing
  • First passage time
  • Iterative algorithm
  • Jump-diffusion
  • Laplace transform
  • Regime-switching

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

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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.",
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