The <i>Fe</i> <i>ar Z Function</i> : modeling asymmetric volatility decay across market shock categories

Purpose This study introduces the Fear Z Function, a behavioral volatility framework that integrates psychological persistence and market momentum into the modeling of VIX decay. The purpose is to move beyond statistical asymmetry toward a model that explicitly captures fear as a dynamic, measurable emotional process. Design/methodology/approach We analyze VIX and S&amp;P 500 data (1990–2025), identify shocks using a 20% threshold and test robustness with sensitivity ranges from 15 to 30%. Model parameters are estimated through constrained nonlinear optimization with clearly defined ranges. We evaluate fit against exponential decay and situate Fear Z relative to EGARCH, HAR-RV and sentiment-based ML approaches. An applied example from the March 2020 COVID-19 shock illustrates the model’s forecasting relevance. Findings The results confirm that fear decays asymmetrically and persists longer under negative momentum (ANOVA p &amp;lt; 0.001). The model replicates the COVID-19 spike with high precision (R2 = 0.94) and correctly forecasted the 2025 VIX decay in real time. Sensitivity analysis shows conclusions are robust across thresholds. Compared to conventional models, Fear Z provides a fit on par or better while adding behavioral interpretability. Originality/value This paper is the first to embed behavioral psychology – loss aversion, negativity bias and emotional inertia – directly into volatility decay modeling. It demonstrates that volatility is not a purely mechanical process but a measurable emotional cycle. The contribution is both theoretical (a structured behavioral model of fear) and practical (a forecasting tool for traders and risk managers).