论文标题
多元二次鹰队过程 - 第一部分：理论分析
Multivariate Quadratic Hawkes Processes -- Part I: Theoretical Analysis
论文作者
论文摘要
事实证明，二次鹰队（Qhawkes）流程有效地繁殖了价格变化的统计数据，捕获了许多风格化的金融市场事实。由最近报道的内源性同伴发生的强烈发生（同时价格上涨了几个资产），我们将Qhawkes扩展到了多元框架（MQHawkes）（Mqhawkes），这些框架正在考虑几种金融资产及其相互作用。假设二次内核写入时间对角分量的总和和排名第一（趋势）贡献，我们研究了内生性比率和由此产生的平稳性条件。然后，我们得出与协方差和反馈内核相关的所谓的Yule-Walker方程，这对于校准经验数据的Mqhawkes过程至关重要。最后，我们研究了该过程的波动率分布，发现与单变量的情况一样，它表现出了幂律行为，并且可以在某些限制情况下进行准确计算的指数。
Quadratic Hawkes (QHawkes) processes have proved effective at reproducing the statistics of price changes, capturing many of the stylised facts of financial markets. Motivated by the recently reported strong occurrence of endogenous co-jumps (simultaneous price jumps of several assets) we extend QHawkes to a multivariate framework (MQHawkes), that is considering several financial assets and their interactions. Assuming that quadratic kernels write as the sum of a time-diagonal component and a rank one (trend) contribution, we investigate endogeneity ratios and the resulting stationarity conditions. We then derive the so-called Yule-Walker equations relating covariances and feedback kernels, which are essential to calibrate the MQHawkes process on empirical data. Finally, we investigate the volatility distribution of the process and find that, as in the univariate case, it exhibits power-law behavior, with an exponent that can be exactly computed in some limiting cases.
