Interest rate derivatives in a CTMC setting: pricing, replication and Ross recovery
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917781806514176 |
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| author | Leung, Tim Lorig, Matthew |
| author_facet | Leung, Tim Lorig, Matthew |
| contents | We consider a financial market in which the short rate is modeled by a continuous time Markov chain (CTMC) with a finite state space. In this setting, we show how to price any financial derivative whose payoff is a function of the state of the underlying CTMC at the maturity date. We also show how to replicate such claims by trading only a money market account and zero-coupon bonds. Finally, using an extension of Ross' Recovery Theorem due to Qin and Linetsky, we deduce the real-world dynamics of the CTMC. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14193 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interest rate derivatives in a CTMC setting: pricing, replication and Ross recovery Leung, Tim Lorig, Matthew Mathematical Finance We consider a financial market in which the short rate is modeled by a continuous time Markov chain (CTMC) with a finite state space. In this setting, we show how to price any financial derivative whose payoff is a function of the state of the underlying CTMC at the maturity date. We also show how to replicate such claims by trading only a money market account and zero-coupon bonds. Finally, using an extension of Ross' Recovery Theorem due to Qin and Linetsky, we deduce the real-world dynamics of the CTMC. |
| title | Interest rate derivatives in a CTMC setting: pricing, replication and Ross recovery |
| topic | Mathematical Finance |
| url | https://arxiv.org/abs/2409.14193 |