Interest rate derivatives in a CTMC setting: pricing, replication and Ross recovery
Mathematical Finance
2024-09-24 v1
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.
Keywords
Cite
@article{arxiv.2409.14193,
title = {Interest rate derivatives in a CTMC setting: pricing, replication and Ross recovery},
author = {Tim Leung and Matthew Lorig},
journal= {arXiv preprint arXiv:2409.14193},
year = {2024}
}