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Interest rate derivatives in a CTMC setting: pricing, replication and Ross recovery

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  • Tim Leung
  • Matthew Lorig

Abstract

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.

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  • Tim Leung & Matthew Lorig, 2024. "Interest rate derivatives in a CTMC setting: pricing, replication and Ross recovery," Papers 2409.14193, arXiv.org.
    • Handle: RePEc:arx:papers:2409.14193
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    File URL: http://arxiv.org/pdf/2409.14193
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