International Review of Business, Trade, and Economics
When Markets Stop Listening: Stochastic Noise Intensity, the Generalized Signal Process, and the Design of Macroprudential Policy
Abstract
Darius Joseph Hanson
This paper extends the dynamic informational asymmetry framework established in Hanson (2025) by treating the noise intensity parameter η not as a fixed exogenous constant but as a time-varying stochastic process with its own governing dynamics [1]. The central limitation of prior models in this literature is that the informational environment itself is treated as stationary [2-5]. In financial crises, it manifestly is not. We introduce a stochastic differential equation for ηt that incorporates mean-reverting drift, stochastic volatility, and Poisson jumps, where jump intensity is endogenously linked to the credit risk state variable λt . We decompose ηt into a systematic component common to all institutions and an idiosyncratic component driven by firm-specific opacity, enabling a cross-sectional theory of noise contagion. Within this generalized framework, we formally derive the noise-dominated threshold η∗ , the level above which the Kalman– Bucy belief-updating mechanism becomes statistically inert and managerial signaling fails regardless of the firm’s true solvency. This threshold generalizes the Strategic Exit Condition introduced in Hanson (2026) by adding a second, noise-triggered channel of institutional failure [6]. We then recast the dominant post-crisis regulatory instruments (mandatory disclosure requirements, the Liquidity Coverage Ratio, stress testing, and emergency liquidity facilities) as η-suppression mechanisms within a unified theoretical framework. Our primary policy contribution is a tiered dynamic activation rule that conditions regulatory intervention on the estimated distance between ηt and η∗ , enabling preemptive macroprudential action before noise-dominated panics force the liquidation of solvent institutions. Calibration against market-based proxies demonstrates that Bear Stearns in March 2008 crossed the noise-dominated threshold primarily through the systematic component of ηt , while the Lehman Brothers failure in September 2008 reflected elevated idiosyncratic noise compounded by genuine deterioration in the latent value process Vt . These findings clarify the appropriate regulatory response for each failure type and carry direct implications for the design of forward-looking macroprudential oversight.