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

2024/09/21 by Tim Leung, Matthew Lorig, Leung, Tim +1
Economics, Econometrics and Finance · #Diverse Scientific and Economic Studies #Economic theories and models #FOS: Economics and business #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2409.14193

openalex publication_date 2024/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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