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

Battle Count: 81

Highly relevant to quantitative trading, particularly for options market making, delta-hedging strategies, and risk management. The paper provides actionable insights: (1) identifies parameter regimes where gamma-squeeze feedback dominates, (2) shows low-beta stocks are disproportionately vulnerable to modest shocks, (3) provides a quantitative stability threshold for monitoring hedging exposure, and (4) offers a tractable simulation framework for stress-testing option positions. However, it lacks empirical validation and does not directly propose trading signals or execution algorithms.

The core model involves a discrete-time recursive simulation with approximately 10-15 interacting equations. Key components include: delta-neutral hedging mechanics (straightforward), beta-normalized surprise calculation (simple), tanh saturation function (standard), position decay with cumulative movement (moderate), and AR(1) stochastic process for option arrivals (standard). The mathematical derivations are accessible to those with graduate-level quantitative finance background. Implementation requires careful handling of the recursive feedback loop, parameter calibration, and numerical stability near the bifurcation boundary. No specialized libraries or hardware are needed beyond standard numerical computing.

The paper provides detailed simulation parameters (λ, G, σ_m, η, ξ, ρ, σ_N, κ, k, S_0, µ values, β values) and full mathematical derivations. However, simulation code and data are only available 'upon reasonable request' from the corresponding author. No public repository is provided. The model is analytically tractable and parameters are explicitly stated, enabling independent replication, but the lack of open-source code reduces reproducibility.