Beta-Dependent Gamma Feedback and Endogenous Volatility Amplification in Option Markets

ArXiv ID: 2511.22766 “View on arXiv”

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.

Keywords: Gamma-Squeeze, Market Maker Hedging, Volatility Amplification, Options, Equities

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: 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.

  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"]