We analyze empirical evidence of flocking stock volatilities according to the Cucker–Smale (C–S) mechanism. By using daily realized volatilities of stocks listed on Dow Jones Industrial Average from January, 2007 to December, 2009, we calibrate key parameters such as time-varying coupling strength, communication weight and stochastic noise in coupling of a benchmark C–S model in Bae et al. (Math Models Methods Appl Sci 25:1299–1335, 2015). Our numerical solutions show that the flocking mechanism explains average volatility dynamics better than a stochastic volatility model without the mechanism over the sample period. The model’s empirical implications are found from cyclicality of Volatility Flocking Index (VFI), an aggregate measure of differences between volatilities. Results from Granger causality tests after vector autoregression estimation show that VFI helps us predict the implied volatility index, and weighted average return of S&P500 Index.

中文翻译：

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金融市场中 Cucker-Smale 机制的波动性聚集

我们根据 Cucker-Smale (C-S) 机制分析了植绒库存波动的经验证据。通过使用 2007 年 1 月至 2009 年 12 月道琼斯工业平均指数上市股票的每日实现波动率，我们校准了 Bae 基准 C-S 模型耦合中的关键参数，如时变耦合强度、通信权重和随机噪声等。（数学模型方法应用科学 25：1299–1335，2015）。我们的数值解决方案表明，在样本期内，群集机制比没有该机制的随机波动率模型更好地解释了平均波动率动态。该模型的实证意义是从波动率聚集指数 (VFI) 的周期性中发现的，VFI 是波动率之间差异的综合度量。