Quantitative Finance

Data-driven analysis of financial risk, volatility, and the mathematics underlying market behavior.

Central to this category is the variance tax, the half-sigma-squared drag on compound returns that explains why volatility matters more than most investors realize. The companion piece on the long volatility premium synthesizes evidence from One River, Goldman Sachs, AQR, and Universa on whether tail hedging is a compensated factor or an expensive insurance policy.

On market structure, It Just Ain’t So challenges the Gaussian assumption underlying standard financial models, examining fat tails and their implications for risk management. The private equity beta analysis tests whether the illiquidity premium survives after adjusting for leverage and mark-to-market smoothing.

Applied work includes tensor-based market modeling as an alternative to Monte Carlo simulation, and the mathematics of provably fair casino games applying probability theory to verifiable randomness.