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

TL;DR

This paper models interest rate derivatives using a finite-state CTMC, providing methods for pricing, replication, and recovering real-world dynamics, thus offering a comprehensive framework for interest rate derivative analysis.

Contribution

It introduces a novel approach to price and replicate interest rate derivatives within a CTMC framework and extends Ross' Recovery Theorem for real-world dynamics inference.

Findings

Pricing formulas for derivatives based on CTMC states

Replication strategies using bonds and money market accounts

Extension of Ross' Recovery Theorem for real-world dynamics

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.