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

TL;DR

This paper presents a theoretical model linking micro-level option hedging behaviors with macro-level market turbulence, explaining how endogenous volatility amplification occurs during gamma-squeeze events, especially affecting low-beta stocks.

Contribution

It introduces a novel framework incorporating beta-dependent volatility normalization and market-maker delta-neutral hedging to explain endogenous volatility amplification.

Findings

Low-beta stocks show strong feedback effects during gamma-squeezes.

The model identifies a stability condition for gamma-squeeze onset.

Nonlinear recursive feedback drives self-reinforcing market dynamics.

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.