Duration vs. Catastrophe: A Survival-Based Decomposition of Financial Fragility via the Clock of Regimes Model*

Abstract

Oscar Linares and Ricards Bulavs

This paper implements the Clock of Regimes (COR) model for analyzing financial fragility through the lens of survival dynamics and ruin probability of the E-mini S&P 500 futures (ES) and the S&P 500 index (SPX) during the 2007-2009 Global Financial Crisis crash. By rejecting the standard assumption of ergodicity, the study aims to embed heavy- tailed regime switching within an open architecture where probability mass—defined as probability accumulated over time—dissipates via regime-specific hazard rates. Fragility decomposes into two channels: duration fragility, where regimes remain persis- tently trapped in unfavorable conditions, and catastrophe fragility, where crisis regimes generate extreme tail losses and rapid wealth destruction. Hazard-induced openness accelerates the buildup of ruin probability in both. Empirical results for the E-mini S&P 500 futures (ES) and the S&P 500 index (SPX) show that Student-t specifications are superior for capturing discontinuous shocks. Findings reveal distinct failure pathways: the SPX exhibits stronger duration fragility through prolonged entrapment (132.14 days), while the ES market demonstrates higher catastrophe fragility with a ruin probability nearly 1.6 times higher over 250 days. We conclude that the COR model offers a tractable framework for quantifying ruin exposure and informing risk management.

PDF