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Linking affine and Levy-driven models to the microstructure of financial markets

将仿射和征费驱动模型与金融市场的微观结构联系起来

基本信息

批准号：
348146459
负责人：
Professor Dr. Martin Keller-Ressel
金额：
--
依托单位：
Institut für Mathematische Stochastik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2017
资助国家：
德国
起止时间：
2016-12-31 至 2019-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/348146459?language=en
关键词：
Linking affine Levy driven models

项目摘要

By now, models based on affine stochastic processes and Lévy processes have become an indispensable tool in financial modeling. To a large extent, these models are used to describe markets on a 'macroscopic' scale - approximately in the range of hours to several years - which is the scale relevant for risk management, as well as for the pricing and hedging of derivatives. On the other hand, a more recent research strand in mathematical finance has focused on 'market microstructure', that is, the dynamics of transactions in financial markets on a much smaller time-scale, in the order of microseconds to minutes. The relevance of this time-scale is given both by the increasing (and much-debated) role of high-frequency trading and by the observation of market anomalies that can only be explained on the level of this microstructure.The goal of this project is to cross these scales and to link affine and Lévy-driven stochastic processes to models of market microstructure. Affine processes serve as a unifying framework for models that include self-exciting effects, such as Hawkes processes with exponential kernel. In addition, we aim to show that even Non-Markovian models that have been proposed for market microstructure, like Hawkes-processes with power-law kernels or fractional diffusions can be embedded into the affine framework by considering processes on infinite-dimensional state spaces. Finally, we will combine certain affine and Lévy-driven models with an economic equilibrium model of high-frequency-trading, in order to obtain a full picture of all market events (the 'limit order book') on the microscopic scale.

目前，基于仿射随机过程和Lévy过程的模型已经成为金融建模中不可缺少的工具。在很大程度上，这些模型用于描述“宏观”规模的市场-大约在几小时到几年的范围内-这是与风险管理以及衍生品定价和对冲相关的规模。另一方面，数理金融学最近的一个研究方向是“市场微观结构”，即金融市场中交易的动态变化在一个小得多的时间尺度上，从微秒到分钟。这个时间尺度的相关性是由高频交易的日益增长的（和备受争议的）作用和只能在这个微观结构的水平上解释的市场异常的观察给出的。本项目的目标是跨越这些尺度，并将仿射和Lévy驱动的随机过程与市场微观结构模型联系起来。仿射过程作为一个统一的框架模型，包括自激效应，如霍克斯过程与指数核。此外，我们的目标是表明，即使是非马尔可夫模型，已提出的市场微观结构，如霍克斯过程与幂律内核或分数扩散可以嵌入到仿射框架，考虑过程的无限维状态空间。最后，我们将结合联合收割机某些仿射和列维驱动的模型与高频交易的经济均衡模型，以获得微观尺度上所有市场事件（“限价订单簿”）的全貌。