英文标题：
《Quadratic Hawkes processes for financial prices》
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作者：
Pierre Blanc, Jonathan Donier, Jean-Philippe Bouchaud
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最新提交年份：
2015
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英文摘要：
We introduce and establish the main properties of QHawkes (\"Quadratic\" Hawkes) models. QHawkes models generalize the Hawkes price models introduced in E. Bacry et al. (2014), by allowing all feedback effects in the jump intensity that are linear and quadratic in past returns. A non-parametric fit on NYSE stock data shows that the off-diagonal component of the quadratic kernel indeed has a structure that standard Hawkes models fail to reproduce. Our model exhibits two main properties, that we believe are crucial in the modelling and the understanding of the volatility process: first, the model is time-reversal asymmetric, similar to financial markets whose time evolution has a preferred direction. Second, it generates a multiplicative, fat-tailed volatility process, that we characterize in detail in the case of exponentially decaying kernels, and which is linked to Pearson diffusions in the continuous limit. Several other interesting properties of QHawkes processes are discussed, in particular the fact that they can generate long memory without necessarily be at the critical point. Finally, we provide numerical simulations of our calibrated QHawkes model, which is indeed seen to reproduce, with only a small amount of quadratic non-linearity, the correct magnitude of fat-tails and time reversal asymmetry seen in empirical time series.
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中文摘要：
我们介绍并建立了QHawkes（“二次”Hawkes）模型的主要性质。QHawkes模型概括了E.Bacry等人（2014）中引入的Hawkes价格模型，允许跳跃强度中的所有反馈效应在过去的收益中是线性和二次的。对纽约证券交易所股票数据的非参数拟合表明，二次核的非对角分量确实具有标准霍克斯模型无法再现的结构。我们的模型展示了两个主要特性，我们认为这对建模和理解波动过程至关重要：第一，该模型是时间反转不对称的，类似于时间演化具有偏好方向的金融市常第二，它产生了一个乘法的厚尾波动过程，我们在指数衰减的情况下详细描述了这个过程，它与连续极限下的皮尔逊扩散有关。本文还讨论了QHawkes过程的其他一些有趣的性质，特别是它们可以产生长内存，而不必处于临界点。最后，我们提供了我们校准的QHawkes模型的数值模拟，该模型确实可以重现，只有少量的二次非线性，在经验时间序列中可以看到正确的厚尾大小和时间反转不对称性。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Trading and Market Microstructure 交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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