arXiv subjects

Arshia Ghasemi

Publications and source records attributed to Arshia Ghasemi.

2 recordsLinked to original sources

arXiv2026

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 good linear dependence on the number of days of accumulation. Mean of the distribution also shows near perfect linear dependence as well. We analyze this phenomenon both analytically and numerically using a modified Jones-Faddy skew t-distribution.

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arXiv2026

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 distribution of stock returns can be effectively split in two -- for gains and losses -- assuming difference in parameters of their respective stochastic volatilities. A modified Jones-Faddy skew t-distribution utilized here allows to reflect this in a single organic distribution which tends to meaningfully capture this asymmetry. We illustrate its application on distribution of daily S&P500 returns, including analysis of its tails.

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