Overview
Markov-switching term structure models (MS-TSM) extend affine and quadratic term structure models with discrete latent regimes that follow a finite-state Markov chain. The regimes shift the parameters of the macro VAR, the short-rate dynamics, the prices of risk, or the conditional volatilities — enabling closed-form (or near closed-form) bond pricing recursions while capturing the time-varying conditional moments and expectations-hypothesis violations that single-regime Gaussian models cannot. The line of work originated with Hamilton-style regime-switching for the short rate (Bansal–Zhou) and was substantially extended by no-arbitrage Gaussian-with-regimes models (Dai–Singleton–Yang, Ang–Bekaert–Wei, Bikbov–Chernov). On the rational-expectations side, Cho–Moreno’s forward solution method provides the determinacy / no-bubble condition machinery that is needed to solve multivariate linear RE models with switching coefficients.
Timeline
- 2002 — Bansal & Zhou (JF): CIR-style square-root model with 2-state Markov regimes, EMM estimation, regime shifts capture the expectations-hypothesis violation.
- 2007 — Dai, Singleton & Yang (RFS): discrete-time Gaussian DTSM with priced factor and regime-shift risks, state-dependent transition probabilities, closed-form bond prices.
- 2008 — Ang, Bekaert & Wei (JF): 3-factor regime-switching decomposition of nominal yields into real rates, expected inflation, and inflation risk premium.
- 2009 — Hansen & Scheinkman (Econometrica): operator/semigroup approach to long-term risk; principal eigenvalue/eigenfunction structure underlies asymptotic pricing in regime-switching environments.
- 2009 — Farmer, Waggoner & Zha (JET): necessary and sufficient conditions for determinacy in forward-looking MSRE models via mean-square stability of sunspot spectral operators. See understanding-markov-switching-rational-expectations-models.
- 2010 — Cho & Moreno (JEDC): forward method generalizes recursive substitution to multivariate linear RE models; defines Forward Convergence Condition (FCC) and No-Bubble Condition (NBC).
- 2010s– — Bikbov & Chernov: monetary policy regimes embedded directly in the Taylor rule of a no-arbitrage TSM (closest published precursor to the Leather-Sagi asset-pricing extension).
- 2016 — Foerster (IER): inflation target switching irrelevant for determinacy; inflation response switching is key; calibrated NK-DSGE with 4 regimes. See monetary-policy-regime-switches-macroeconomic-dynamics.
- 2017 — Hayashi (EL): LRTP is sufficient only under regime-independent solutions. See long-run-taylor-principle-revisited.
- 2020 — Cho (JET): MOD method provides complete MSRE classification (determinacy, indeterminacy, no stable solution) using only the most stable MSV solution. See determinacy-classification-markov-switching-rational-expectations.
Seminal works
- bansal-zhou-2002-term-structure-regime-shifts
- dai-singleton-yang-2007-regime-shifts-term-structure
- ang-bekaert-wei-2008-real-rates-expected-inflation
- cho-moreno-2010-forward-method-rational-expectations
- bikbov-chernov-monetary-policy-regimes-term-structure
SOTA tracker
- Closed-form bond prices under regime switching: well-developed (DSY 2007, ABW 2008).
- Multivariate RE solution with switching coefficients: Cho-Moreno forward method is the standard tool; relies on FCC + NBC for uniqueness. Cho (2020) MOD method provides necessary-and-sufficient classification; forward method coincides with MOD in practice.
- Joint identification of priced regimes vs filtered macro state: still hard; state-dependent transition probabilities (DSY) helps but adds free parameters.
Open problems
- Likelihood evaluation with both continuous-state filtering and discrete-state inference is exponential in horizon length without Rao-Blackwellization (see switching-state-estimation).
- Identifying priced regime risk separately from regime-induced volatility shifts remains econometrically delicate.
- Most models live entirely on the bond side; extending no-arbitrage MS-TSM to other asset classes (equities, real estate) requires additional structure — see commercial-real-estate-pricing-regimes.
- Joint identification of regime-conditional risk prices and physical transition probabilities under short samples.
- Mapping latent regimes onto observable monetary policy / inflation regimes without ad hoc identifying restrictions.
My position
For the CRE asset-pricing project this topic supplies the macro / yield half of the model. The Leather–Sagi setup uses a Cho–Moreno forward solution to a Markov-switching NK model, then prices CRE cap rates via no-arbitrage and exponential-quadratic Riccati recursions on top of the resulting risk-neutral macro VAR. So this topic is methodological infrastructure rather than the punchline. Ang–Bekaert–Wei is the canonical empirical reference for “regime-switching affine pricing actually works on real Treasury data.”
Research gaps
- Quadratic / exponential-quadratic asset pricing under multivariate Markov switching is much less developed than the affine case (covered by commercial-real-estate-pricing-regimes).
- Estimation under simulated DGP for MS-TSM with full-likelihood (RBPF) is a small literature; most published estimations use EMM, GMM, or pseudo-likelihoods.
- Identification under absorbing / transient regimes (e.g., monetary policy regime changes that are essentially permanent over a sample) is fragile — open problem.
- Regime-switching models with more than two binary chains (i.e. compound regimes) are largely unexplored in the public bond pricing literature; the CRE project’s 4-compound-regime construction sits in this gap.
- The interaction between regime-switching pricing and particle-filter / RBPF estimation is not well documented in the bond literature.