We assess the impact of trade fragmentation in equity markets using volatility networks following the volatility-of-volatility (VoV) approach. VoV networks offer an original method for measuring and visualizing the common component of volatilities. We use topological distance and connectivity indicators describing their structure as alternative proxies of VoV. Further, we use panel tests to apply threshold effects regression models on French equity market data after the introduction of MiFID, both at portfolio level and asset level. We show that market fragmentation yields a reduction in VoV, corresponding to both a contraction of volatility networks and a change in their structure. This effect strengthens in the stabilizing fragmentation regime compared to the increased fragmentation regime. Since VoV has been shown to predict stock markets returns, this original finding is widely relevant to market operators, regulators and public authorities.

我们按照波动率的波动率 (VoV) 方法，使用波动率网络评估股票市场贸易分散的影响。VoV 网络提供了一种测量和可视化波动率常见组成部分的原始方法。我们使用拓扑距离和连接性指标来描述其结构作为 VoV 的替代代理。此外，我们在引入 MiFID 后，使用面板测试对法国股市数据应用阈值效应回归模型，无论是在投资组合层面还是在资产层面。我们表明，市场碎片化会导致 VoV 减少，这与波动性网络的收缩及其结构的变化相对应。与增加的碎片状态相比，这种效应在稳定碎片状态中增强。由于 VoV 已被证明可以预测股票市场回报，因此这一原始发现与市场运营商、监管机构和公共当局广泛相关。