Quantitative Finance

Financial markets break down in predictable ways during stress. When asset correlations spike toward 1.0 during crises, covariance matrices lose rank and risk models struggle. When liquidity evaporates, pricing engines hit undefined states. Standard fixes like eigenvalue floors, $\epsilon$-regularization, or arbitrary caps solve the immediate numerical problem but introduce bias that compounds through your models. This often masks the true extent of tail risk.

ZeroProofML takes a different approach. It acknowledges that operations like matrix inversion ($A^{-1}$) and derivative pricing are fundamentally rational problems ($P/Q$). When the determinant approaches zero, the system enters a singular regime. Instead of smoothing this warning signal away with arbitrary floors, ZeroProofML uses Signed Common Meadows (SCM) to model the singularity structure explicitly. The Scale-Detached Gradient estimator allows the model to learn the dynamics of the crisis (the asymptotic approach to instability) without numerical collapse.

Potential applications:

• Portfolio Risk: Inverting singular covariance matrices during stress events. SCM handles the transition where the determinant vanishes, preserving the structural warning signal that smoothed models erase.
• Options Trading: Pricing derivatives consistently through expiry when Greeks (like Gamma) diverge. SCM models the vertical asymptote, eliminating the ad-hoc caps that create arbitrage opportunities.
• Credit Modeling: Estimating default probabilities for low-default portfolios where the denominator (event count) approaches zero, avoiding regulatory-questionable bias.
• Execution Algorithms: Maintain stable liquidity metrics when markets thin out, capturing regime changes that smoothed models miss.