We examine the clustering behavior of price and variance jumps using high-frequency data, modeled as a marked Hawkes process (MHP) embedded in a bivariate jump-diffusion model with intraday periodic effects. We find that the jumps of both individual stocks and a broad index exhibit self-exciting behavior. The three dimensions of the model, namely positive price jumps, negative price jumps, and variance jumps, impact one another in an asymmetric fashion. We estimate model parameters using Bayesian inference by Markov Chain Monte Carlo, and find that the inclusion of the jump parameters improves the fit of the model. When we quantify the jump intensity and study the characteristics of jump clusters, we find that in high-frequency settings, jump clustering can last between 2.5 and 6 hours on average. We also find that the MHP generally outperforms other models in terms of reproducing two cluster-related characteristics found in the actual data.

中文翻译：

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使用标记霍克斯过程对价格和方差跳跃聚类建模

我们使用高频数据检查价格和方差跳跃的聚类行为，将其建模为嵌入具有日内周期性效应的双变量跳跃扩散模型中的标记霍克斯过程 (MHP)。我们发现个股和广泛指数的跳跃都表现出自激行为。该模型的三个维度，即正价格跳跃、负价格跳跃和方差跳跃，以不对称的方式相互影响。我们通过马尔可夫链蒙特卡洛使用贝叶斯推理估计模型参数，发现跳跃参数的包含提高了模型的拟合度。当我们量化跳跃强度并研究跳跃集群的特征时，我们发现在高频设置下，跳跃集群平均可以持续 2.5 到 6 小时。