The Fear Generating Function: A Behavioral Model of VIX Decay with Momentum-Conditioned Persistence

We introduce the Fear Generating Function (FGF), a behavioral model of volatility that captures asymmetric fear decay following market shocks. The model incorporates a momentum-sensitive persistence parameter, predicting longer fear duration under negative market momentum. Using VIX and S&P 500 data from 2015–2025, we identify 38 systematic volatility shock events and estimate decay durations under a rule-based framework. Regression analysis with standard errors provides statistically significant support for the model’s central prediction that negative momentum regimes are associated with longer volatility persistence. Robustness checks across alternative momentum windows and shock thresholds confirm the stability of this relationship. A benchmark comparison with a purely exponential decay specification shows that incorporating behavioral persistence improves duration prediction. We also include a time-stamped illustration using a March 2025 volatility spike to demonstrate operational use. The FGF offers a structured behavioral framework for modeling the temporal dynamics of market fear.