摘要翻译：
我们在维1（对于单个资产）和维2（对于一对资产）中引入了一个新的随机模型来研究资产价格在逐节拍水平上的变化。该结构基于标记点过程，并依赖于Hawkes引入的线性自激和相互激励的随机强度。我们将计算过程与资产价格的正向和负向跳跃联系起来。通过适当地同时耦合几种资产价格上行和下行变化的随机强度，我们可以再现微观噪声（即在几秒钟到几分钟的水平上强烈的微观均值逆转）和Epps效应（即微观尺度上增量的去相关），同时在大尺度上保持标准的布朗扩散行为。更有效地，我们得到了均值签名图的解析闭式公式和两个价格增量的相关性，从而能够跨尺度跟踪均值回复的影响，直到模型的扩散极限。我们证明了在几种情况下，理论结果与欧洲-外滩和欧洲-BOBL期货的经验拟合是一致的。
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英文标题：
《Modeling microstructure noise with mutually exciting point processes》
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作者：
E. Bacry, S. Delattre, M. Hoffmann and J.F. Muzy
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最新提交年份：
2011
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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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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
  We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on linear self and mutually exciting stochastic intensities as introduced by Hawkes. We associate a counting process with the positive and negative jumps of an asset price. By coupling suitably the stochastic intensities of upward and downward changes of prices for several assets simultaneously, we can reproduce microstructure noise (i.e. strong microscopic mean reversion at the level of seconds to a few minutes) and the Epps effect (i.e. the decorrelation of the increments in microscopic scales) while preserving a standard Brownian diffusion behaviour on large scales. More effectively, we obtain analytical closed-form formulae for the mean signature plot and the correlation of two price increments that enable to track across scales the effect of the mean-reversion up to the diffusive limit of the model. We show that the theoretical results are consistent with empirical fits on futures Euro-Bund and Euro-Bobl in several situations.
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PDF链接：
https://arxiv.org/pdf/1101.3422