arXivDaily arXiv每日学术速递 周一至周五更新
2606.20145 2026-06-19 q-fin.ST cond-mat.stat-mech physics.data-an q-fin.MF q-fin.RM 新提交

Trends, Volatility, Correlations, and Critical Phenomena in Financial Markets

金融市场中的趋势、波动率、相关性和临界现象

Sara A. Safari, Christoph Schmidhuber

AI总结 基于当前市场趋势预测未来波动率和相关性,发现趋势强度与波动率、相关性呈二次关系,改进风险预测并支持临界点晶格气体模型。

Comments 31 pages, 9 figures

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AI中文摘要

我们基于金融市场的当前趋势预测未来的波动率和相关性。这补充了先前的工作,该工作通过当前趋势强度的三次多项式来建模未来预期收益。经验上,我们观察到在强烈上升或下降趋势期间,波动率和相关性往往逐日增加。这种效应在下降趋势中尤为显著。它可以通过当前趋势强度的二次多项式精确量化,这细化了波动率和相关性的常见均值回归模型。我们的结果通过考虑市场趋势改进了市场风险的预测。它们也支持最近一项将金融市场建模为接近其临界点的晶格气体的提议。

英文摘要

We forecast future volatilities and correlations of financial markets based on the current trends in these markets. This complements previous work that models future expected returns by a cubic polynomial of the current trend strength. Empirically, we observe that volatilities and correlations tend to increase day after day in times of strong up- or down-trends. This effect is particularly pronounced in down-trends. It can be accurately quantified by quadratic polynomials of today's trend strengths, which refine common mean-reversion models of volatilities and correlations. Our results improve the prediction of market risk by accounting for market trends. They also support a recent proposal to model financial markets by a lattice gas near its critical point.