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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| Vydáno v: | Journal of computational and applied mathematics Ročník 294; s. 177 - 195 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier B.V
01.03.2016
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| ISSN: | 0377-0427, 1879-1778 |
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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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| AbstractList | 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. |
| Author | Kim, Jerim Wee, In-Suk Kim, Bara |
| Author_xml | – sequence: 1 givenname: Jerim surname: Kim fullname: Kim, Jerim email: jerimkim@yongin.ac.kr organization: Department of Business Administration, Yong In University, 134 Yongindaehak-ro, Cheoin-gu, Yongin-si, Gyeonggi-do, 449-714, Republic of Korea – sequence: 2 givenname: Bara surname: Kim fullname: Kim, Bara email: bara@korea.ac.kr organization: Department of Mathematics, Korea University, 145, Anam-ro, Seongbuk-gu, Seoul, 136-701, Republic of Korea – sequence: 3 givenname: In-Suk surname: Wee fullname: Wee, In-Suk email: iswee@korea.ac.kr organization: Department of Mathematics, Korea University, 145, Anam-ro, Seongbuk-gu, Seoul, 136-701, Republic of Korea |
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| Keywords | 65C40 Regime-switching First passage time Iterative algorithm Defaultable bond pricing 60J25 Laplace transform Jump–diffusion 60J22 |
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| SubjectTerms | 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 |
| Title | Iterative algorithm for the first passage time distribution in a jump–diffusion model with regime-switching, and its applications |
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