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Synapse
March 29, 2026Open Access

Exact Volatility Explosion and Contagion in Financial Markets via the F lambda Class

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Authors

JBJudicael Brindel

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Overview

Analytical framework captures volatility explosion during market stress, indicating potential crash conditions.

Key Points

  • To investigate the dynamics of volatility during market stress and establish a mathematical framework for understanding this phenomenon.
  • Derived a closed-form expression for time to volatility explosion using the F_lambda class.
  • Calibrated the model on historical VIX crises in 2008, 2018, and 2020.
  • Developed a PDE model for cross-asset contagion with exact solutions using Gaussian convolution.
  • Identified a universal scaling law for time to crash as lambda approaches zero.
  • Established an analytical boundary in (lambda, sigma0) space separating stable and crash regimes.
  • Created a real-time early warning indicator for monitoring volatility levels.

Cite This Study

Judicael Brindel (2026) studied this question.

synapsesocial.com/papers/69c8c43ede0f0f753b39ee91https://doi.org/10.5281/zenodo.19243202
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