McBride
Mathematician turned quant researcher. My graduate work at UC Santa Cruz focused on algebraic topology, culminating in a thesis extending UMAP — a manifold learning algorithm grounded in topological data analysis. I now apply that foundation to derivatives pricing and volatility modeling, building end-to-end research infrastructure from raw market data to calibrated stochastic models.
Research Projects
Expiry ↗
IV ↑
End-to-end derivatives research platform calibrated to live SPY options data. Fits all five Heston parameters to 1,542 market contracts via two-stage differential evolution, then prices arbitrary options and computes full Greeks across the volatility surface using Gil-Pelaez Fourier inversion.
Graduate thesis building rigorous theoretical foundations for UMAP — connecting Riemannian geometry, fuzzy simplicial sets, and topological data analysis. Establishes formal guarantees on topological faithfulness of embeddings and bounds embedding quality via Gromov–Hausdorff distance. Includes interactive point-cloud visualizations and comparison against PCA and t-SNE.
Published research establishing sharp bounds between the Gromov–Hausdorff distance and the simpler Hausdorff distance for compact metric spaces. Provides computable, tight two-sided certificates for metric space similarity — with direct applications to topological data analysis, shape comparison, and certifying UMAP embedding quality.