Research
Most people accept the concept of randomness in the world. What if randomness was just a lack of information, a concept that only actually affects the minority of physics of our world? If we refuse this for just a second, it becomes evident that we merely need the pieces to solve our puzzle. After all, as you place more and more pieces into a puzzle, the picture does grow clearer.
Mathematics has its beauty. As does its application to financial time series. I have applied a vast number of branches in order to grow ever-closer to completing the puzzle. And the beauty of what I have found is overwhelming.
— Cormac Lydon
The Fisher-Rao metric on the space of probability distributions induces non-zero curvature. We exploit the divergence between Euclidean and Riemannian computations as a novel class of trading signals.
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Geodesic regression, Fréchet means, and parallel transport on the Gaussian manifold. Parameter decay rates explained by holonomy accumulation via the Ambrose-Singer theorem.
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Jump-diffusion processes, local and stochastic volatility surfaces, rough volatility, and realized variance decomposition applied to futures markets.
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Persistent homology and Betti curves for identifying structural invariants in high-dimensional price data that persist across temporal scales.
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Marchenko-Pastur eigenvalue filtering for covariance estimation, signal-noise separation, and spectral methods including Fourier and Hilbert-Huang decomposition.
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Distribution-level distance metrics for regime classification, non-parametric signal construction, and gradient flow models of distributional evolution.
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Iterated integral features capturing the geometry of sequential price paths, providing feature-invariant encodings for strategy selection.
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Ollivier-Ricci and Forman-Ricci curvature on correlation networks, with discrete Ricci flow for detecting structural fragmentation preceding regime transitions.
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Locally stationary processes with measurable validity horizons. The bias-variance tradeoff inverts under non-stationarity: deliberately local models with matched lifecycles dominate generalized models.
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Cormac Lydon · Lydon Quantitative Research · April 2026
Introduces seven divergence predicates measuring the gap between flat-space and curved-space computations on rolling windows of financial time series. Proves non-triviality for all empirically observed return distributions, connects parameter decay to holonomy via the Ambrose-Singer theorem, and establishes minimax optimality of daily recalibration.
Cormac Lydon · Lydon Quantitative Research · April 2026
Shows that under non-stationary dynamics with measurable validity horizons, the classical bias-variance tradeoff inverts: deliberately overfit models with matched lifecycles provably dominate generalized models. Formalizes a non-stationary bias-variance decomposition and proves that standard cross-validation conflates noise overfitting with regime fitting.
Autonomous strategy factory for CME futures. The system mines, validates, deploys, and discards strategies on a daily cycle — each calibrated to local market dynamics and replaced before its validity horizon expires. Mathematical signal generation spans multiple branches of pure and applied mathematics.
Prediction market and sports analytics platform. Integrates multiple probabilistic models for event forecasting across prediction markets and sports, with bankroll management informed by information-theoretic sizing criteria.