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

Paper: arXiv 2409.14193

Authors: 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.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a solid theoretical exploration of short-rate modeling using continuous-time Markov chains, establishing closed-form matrix pricing, replication strategies, and real-world recovery via Ross Recovery. However, it is purely theoretical with virtually no empirical testing, backtesting, or real market data validation.

Research Flowchart

  flowchart TD
    A[Goal: Price & replicate interest rate derivatives and recover real-world dynamics via CTMC] --> B[Inputs: Short rate modeled as a finite-state CTMC]
    B --> C[Derive pricing formulas for derivatives via matrix exponentials]
    B --> D[Construct replication strategies using Money Market Account & Zero-Coupon Bonds]
    B --> E[Apply Qin-Linetsky extension of Ross Recovery Theorem]
    C --> F[Key Outcomes: Exact pricing, full market replication, and real-world probability dynamics]
    D --> F
    E --> F