Overview
This wiki is built around a single research line: pricing commercial real estate (CRE) cap rates inside a New-Keynesian / DSGE-style macro model whose monetary policy and wage-rigidity parameters switch according to two independent binary Markov chains (4 compound regimes). The pricing kernel is no-arbitrage with regime-dependent prices of risk, and the asset prices for CRE come out of an exponential-quadratic form whose coefficients satisfy a system of coupled Riccati recursions over an unbounded horizon. The macro side is solved via the Cho–Moreno forward method for multivariate linear rational-expectations models with switching coefficients, with the no-bubble condition (NBC) acting as a hard determinacy gate.
The wiki organizes the literature into four supporting topics:
- markov-switching-term-structure-models — DSY 2007, BZ 2002, ABW 2008, Bikbov–Chernov, Cho–Moreno 2010. The macro/yield half of the model.
- commercial-real-estate-pricing-regimes — Leather–Sagi (the central paper), the Riccati derivation note, Hansen–Scheinkman 2009, and Ghysels’ CRE forecasting handbook chapter. The CRE half.
- markov-jump-linear-systems-control-filtering — Costa–Fragoso–Marques textbook, Moon–Başar 2016. Stability theory, coupled Riccati existence, and risk-sensitive impossibility results.
- switching-state-estimation — Murphy 1998, Mazor (IMM survey), Crouse / Runnalls (Gaussian mixture reduction). The filtering machinery used to evaluate the model likelihood (Rao-Blackwellized particle filter on regime histories).
A handful of tangential papers (RL / generalized Bellman methods) sit outside these topics as standalone references.
Core areas
Macro RE with switching coefficients
NK macro core (output gap, inflation, short rate) with Taylor rule and wage Phillips curve whose coefficients switch across the 4 compound regimes. Solved via Cho–Moreno forward recursion; FCC + NBC act as the determinacy / no-bubble gate.
Term-structure pricing with regimes
Affine bond prices with regime-dependent state vectors are the warm-up. Closed forms exist under the DSY/ABW Gaussian-with-regimes setup. The CRE extension breaks affinity because the cap-rate observation involves products of state variables, producing exponential-quadratic factors.
Exponential-quadratic CRE cap-rate pricing
Coupled Riccati recursions in (A, B, C) coefficients over unbounded horizon, one per regime, with regime-conditional risk-neutral expectations. The asymptotic behavior is governed by the spectral radius of a regime-switching second-moment operator (Hansen– Scheinkman framework). Convergence is fragile under near-absorbing monetary regimes; state-dependent T_bar requirements arise (Apartment is the slow asset).
MJLS theoretical infrastructure
Mean-square stability (CFT Ch.3), coupled algebraic Riccati existence (CFT Ch.4 + Appendix A), MJLS filtering with mode known vs unknown (CFT Ch.5), risk-sensitive impossibility (Moon–Başar). These results justify the determinacy check, the asymptotic pricing convergence, and the per-particle Kalman recursions used in the RBPF.
Switching state filtering
Mode-unknown filtering has M^t-component optimal Gaussian mixture posterior. Three
families of approximations: moment-collapsing (GPB1/GPB2/IMM), selection/sampling (RBPF
in particular), and variational. The CRE project uses RBPF as the production likelihood
evaluator (≈350 ms/eval at N=3000), with the Hamilton filter as a deterministic surrogate
(≈2 ms/eval) for early-stage screening. Hamilton-optimal ≠ RBPF-optimal because the
Hamilton surrogate ignores the cap-rate panel.
Evolution
The line of work in this wiki builds on three independent traditions:
- Term-structure econometrics (Hamilton 1989, Bansal–Zhou 2002, DSY 2007, ABW 2008): established that regime switching is necessary to capture the time-varying conditional moments of yields.
- Rational-expectations solution methods (Sims 2002, Cho–Moreno 2010): provided the algorithmic machinery for solving multivariate linear RE models with non-trivial cross-equation restrictions and switching coefficients.
- MJLS control / filtering theory (Costa–Fragoso–Marques textbook line, plus the particle-filter / RBPF literature from Doucet–de Freitas–Gordon, Liu, Murphy): provided the stability and coupled-Riccati existence results plus the filtering algorithms needed for likelihood evaluation.
The Leather–Sagi paper synthesizes all three for the CRE asset-pricing problem.
Current frontiers
- Global optimization on simulated DGP (project’s next milestone): a formal global optimization pipeline is being designed to close the cold-Sobol-start global recovery gap. Local recovery already works.
- Curvature / identification at the incumbent: extreme sloppiness (cond ≈ 10²⁵–10²⁶ on the Hamilton surrogate) plus a forward-FD diagonal-stencil bug at non-critical points has reduced the curvature analysis to DIAGNOSTIC_ONLY. Central-FD rerun pending.
- Operator-floor null hypothesis (Exp 12 follow-up): the geometric tail operator
η_H · r/(1-r)with a single globalris the leading hypothesis for the real bottleneck in the per-period Riccati horizon detector — not yet proven. - Real-data MAP: the simulated-data validation arc is closed; the real-data application using NCREIF / Green Street / RCA cap-rate panels is unfinished.
Key references
The wiki itself is the index. Highest-priority pages to read:
- leather-sagi-markov-switching-cre-asset-pricing — the central paper.
- riccati-equations-leather-sagi — full pricing-recursion derivation.
- cho-moreno-2010-forward-method-rational-expectations — RE solution method.
- hansen-scheinkman-2009-long-term-risk-operator-approach — long-run pricing theory.
- dai-singleton-yang-2007-regime-shifts-term-structure — closest published predecessor.
- murphy-1998-switching-kalman-filters — filtering taxonomy.
- costa-fragoso-marques-mjls-textbook — MJLS theoretical reference.