Papers, ranked by score

Ordered by a blend of empirical rigor (60%) and math complexity (40%).

Broken Symmetry, Conservation Law, and Scaling in Accumulated Stock Returns -- a Modified Jones-Faddy Skew t-Distribution Perspective

We analyze historic S&P500 multi-day returns: from daily returns to those accumulated over up to ten days. Despite symmetry breaking between gains and losses in the distribution of returns, resulting in its positive mean and negative skew, realized variance (volatility squared) exhibits remarkably g

Holy Grail Math 8 Rigor 6.5 ·  April 1, 2026

Broken Symmetry of Stock Returns -- a Modified Jones-Faddy Skew t-Distribution

We argue that negative skew and positive mean of the distribution of stock returns are largely due to the broken symmetry of stochastic volatility governing gains and losses. Starting with stochastic differential equations for stock returns and for stochastic volatility we argue that the distributio

Lab Rats Math 8 Rigor 3 ·  December 29, 2025

From a Hierarchy of Stochastic Differential Equations to a Hierarchy of Generalized Beta Distributions

We introduce a mean-reverting stochastic differential equation with a three-component stochastic term and show that it generates a hierarchy of steady-state (stationary) distributions. At the top level, the hierarchy is described by a modified-Beta distribution, while one- and two-parameter reductio

Lab Rats Math 9 Rigor 2 ·  October 7, 2026

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