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Time Varying Moments, Regime Switch, and Crisis Warning: The Birth-Death Process with Changing Transition Probability

Abstract:The sub-prime crisis in the U.S. reveals the limitation of diversificationstrategy based on mean-variance analysis. A regime switch and a turning point can be observed using a high moment representation andtime-dependent transition probability. Up-down price movements are induced by interactions among agents, which can be described by thebirth-death (BD) process. Financial instability is visible by dramatically increasing 3rd to 5th moments one-quarter before and during the crisis.The sudden rising high moments provide effective warning signals of a regime-switch or a coming crisis. The critical condition of a marketbreakdown can be identified from nonlinear stochastic dynamics. The master equation approach of population dynamics provides a unified theory of a calm and turbulent market.

Key Words: high moments, birth-death process, transition probability,regime switch, crisis warning

PACS: 89.65.Gh, 05.45.Tp, 05.10.Gg, 89.75.-k

Time varying moments regime switch and crisis warning The birth–death process with changing transition probability

 

 

 

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