Infinite-variance estimators resist both calm and crisis, stabilizing margin requirements

Evidence

Even quite substantial fluctuations in market volatility have limited, slow effects on statistical estimators of the parameters of Levy distributions with infinite variance. In calm periods, estimates of the probabilities of extreme events do not go down much, so margin requirements are not reduced substantially. When extreme events do happen, Levy estimators are also affected only relatively modestly, because Levy distributions with infinite variance “assume” that the probabilities of such events happening are substantial. — Donald MacKenzie, An Engine, Not a Camera, 940

Categorization

• XREF: This connects to the broader literature on model-induced stability (e.g., how parameter choices can dampen or amplify systemic volatility), echoing MacKenzie’s discussion of how market models feed back into market dynamics. — connects to: Spreading’s robustness to volatility estimates made it viable for floor traders — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 734; Levy distributions yield more stable estimates of extreme moves than variance-based methods — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 937; Post-1987 margin rules replaced log-normal pricing assumptions with fat-tailed stable distributions — Donald MacKenzie & Yuval Millo, Constructing a Market, Performing Theory, 170

Broader Connections

• Levy distributions yield more stable estimates of extreme moves than variance-based methods #corroborates (0.85) — Donald MacKenzie, An Engine, Not a Camera, 937