Paper: arXiv 2511.22766

Authors: Haoying Dai

Abstract

We develop a theoretical framework that aims to link micro-level option hedging and stock-specific factor exposure with macro-level market turbulence and explain endogenous volatility amplification during gamma-squeeze events. By explicitly modeling market-maker delta-neutral hedging and incorporating beta-dependent volatility normalization, we derive a stability condition that characterizes the onset of a gamma-squeeze event. The model captures a nonlinear recursive feedback loop between market-maker hedging and price movements and the resulting self-reinforcing dynamics. From a complex-systems perspective, the dynamics represent a bounded nonlinear response in which effective gain depends jointly on beta-normalized shock perception and gamma-scaled sensitivity. Our analysis highlights that low-beta stocks exhibit disproportionately strong feedback even for modest absolute price movements.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents advanced mathematical derivations with recursive feedback loops and stability conditions, but lacks any backtesting, code, or empirical data implementation, focusing purely on theoretical modeling.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Model Gamma-Squeeze & Vol Amplification"] --> B["Methodology:<br>Theoretical Framework & Stability Analysis"]
  B --> C["Inputs:<br>Beta, Option Gamma, Liquidity"]
  C --> D["Computation:<br>Delta-Neutral Hedging Loop"]
  D --> E{"Stability Condition<br>Met?"}
  E -- No --> F["Outcomes:<br>Stable Market, Limited Feedback"]
  E -- Yes --> G["Outcomes:<br>Gamma-Squeeze, Endogenous Vol Amplification"]