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平均场 Hawkes 订单流与临界随机波动率

文章 arXiv papers · 作者: Paolo Dai Pra et al.
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总结

本文介绍一种基于智能体的逐笔价格形成模型。每个智能体的买卖订单遵循相互激励的 Hawkes 过程，而平均场交互将不同智能体的活动联系起来，并产生相关的订单量。这种交互旨在表示市场订单流中的羊群效应和传染效应等影响。

主要结果涉及临界参数设定下的大规模群体极限：总价格可由带有杠杆效应的随机波动率模型近似，且波动率的均值回归速度快于线性速度。作者将这种更快的均值回归与既有计量经济学证据以及早期研究报告的多重分形行为联系起来。本文是理论研究，没有提供具体市场数据、校准或交易测试，因此它解释的是一种可能机制，而非证明某种策略可用于实际部署。

核心观点

  • 相互激励的 Hawkes 过程表示智能体买卖订单的到达。
  • 平均场交互产生跨智能体相关性，可能反映羊群效应和传染效应。
  • 在临界参数设定下，总价格的极限具有随机波动率和杠杆效应。
  • 由此得到的波动率过程具有快于线性的均值回归，作者将其与多重分形价格行为联系起来。
  • 本文给出的是建模结果，而非经过校准或测试的交易策略。

标签

市场微观结构波动率统计学
全文
# A stochastic volatility approximation for a tick-by-tick price model with mean-field interaction


# A stochastic volatility approximation for a tick-by-tick price model with mean-field interaction









We consider a tick-by-tick model of price formation, in which buy and sell orders are modeled as self-exciting point processes (Hawkes process), similar to the one in [Bacry, Delattre, Hoffmann, Muzy, Modelling microstructure noise with mutually exciting point processes, Quantitative Finance, 2013] and [El Euch, Fukasawa, Rosenbaum, The microstructural foundations of leverage effect and rough volatility, Finance and Stochastics, 2018]. We adopt an agent based approach by studying the aggregation of a large number of these point processes, mutually interacting in a mean-field sense. The financial interpretation of the model is that of an asset on which several labeled agents place buy and sell orders following these point processes, influencing the price. The mean-field interaction introduces positive correlations between order volumes coming from different agents that reflect features of real markets such as herd behavior and contagion. When the large scale limit of the aggregated asset price is computed, if parameters are set to a critical value, a singular phenomenon occurs: the aggregated model converges to a stochastic volatility model with leverage effect and faster-than-linear mean reversion of the volatility process. The faster-than-linear mean reversion of the volatility process is supported by econometric evidence, and we have linked it in [Dai Pra, Pigato, Multi-scaling of moments in stochastic volatility models, Stochastic Processes and their Applications, 2015] to the observed multifractal behavior of assets prices and market indices. This seems connected to the Statistical Physics perspective that expects anomalous scaling properties to arise in the critical regime.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。