{"title":"资产价格分析的随机方法","authors":"Michael Sekatchev, Zhengxiang Zhou","doi":"arxiv-2407.06745","DOIUrl":null,"url":null,"abstract":"In this project, we propose to explore the Kalman filter's performance for\nestimating asset prices. We begin by introducing a stochastic mean-reverting\nprocesses, the Ornstein-Uhlenbeck (OU) model. After this we discuss the Kalman\nfilter in detail, and its application with this model. After a demonstration of\nthe Kalman filter on a simulated OU process and a discussion of maximum\nlikelihood estimation (MLE) for estimating model parameters, we apply the\nKalman filter with the OU process and trailing parameter estimation to real\nstock market data. We finish by proposing a simple day-trading algorithm using\nthe Kalman filter with the OU process and backtest its performance using\nApple's stock price. We then move to the Heston model, a combination of\nGeometric Brownian Motion and the OU process. Maximum likelihood estimation is\ncommonly used for Heston model parameter estimation, which results in very\ncomplex forms. Here we propose an alternative but easier way of parameter\nestimation, called the method of moments (MOM). After the derivation of these\nestimators, we again apply this method to real stock data to assess its\nperformance.","PeriodicalId":501139,"journal":{"name":"arXiv - QuantFin - Statistical Finance","volume":"27 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stochastic Approaches to Asset Price Analysis\",\"authors\":\"Michael Sekatchev, Zhengxiang Zhou\",\"doi\":\"arxiv-2407.06745\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this project, we propose to explore the Kalman filter's performance for\\nestimating asset prices. We begin by introducing a stochastic mean-reverting\\nprocesses, the Ornstein-Uhlenbeck (OU) model. After this we discuss the Kalman\\nfilter in detail, and its application with this model. After a demonstration of\\nthe Kalman filter on a simulated OU process and a discussion of maximum\\nlikelihood estimation (MLE) for estimating model parameters, we apply the\\nKalman filter with the OU process and trailing parameter estimation to real\\nstock market data. We finish by proposing a simple day-trading algorithm using\\nthe Kalman filter with the OU process and backtest its performance using\\nApple's stock price. We then move to the Heston model, a combination of\\nGeometric Brownian Motion and the OU process. Maximum likelihood estimation is\\ncommonly used for Heston model parameter estimation, which results in very\\ncomplex forms. Here we propose an alternative but easier way of parameter\\nestimation, called the method of moments (MOM). After the derivation of these\\nestimators, we again apply this method to real stock data to assess its\\nperformance.\",\"PeriodicalId\":501139,\"journal\":{\"name\":\"arXiv - QuantFin - Statistical Finance\",\"volume\":\"27 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - QuantFin - Statistical Finance\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2407.06745\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - QuantFin - Statistical Finance","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.06745","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
在本项目中,我们建议探索卡尔曼滤波器在估计资产价格方面的性能。我们首先介绍一个随机均值回复过程,即 Ornstein-Uhlenbeck (OU) 模型。之后,我们将详细讨论卡尔曼滤波器及其在该模型中的应用。在演示了卡尔曼滤波器在模拟 OU 过程中的应用,并讨论了用于估计模型参数的最大似然估计 (MLE)之后,我们将卡尔曼滤波器与 OU 过程和跟踪参数估计一起应用于真实股市数据。最后,我们提出了一种使用卡尔曼滤波和 OU 过程的简单日内交易算法,并使用苹果公司的股票价格对其性能进行了回溯测试。然后,我们转向赫斯顿模型,这是几何布朗运动和 OU 过程的结合。最大似然估计法通常用于赫斯顿模型参数估计,这会导致非常复杂的形式。在此,我们提出了另一种更简便的参数估计方法,即矩法(MOM)。在推导出这些估计方法后,我们再次将该方法应用于真实股票数据,以评估其性能。
In this project, we propose to explore the Kalman filter's performance for
estimating asset prices. We begin by introducing a stochastic mean-reverting
processes, the Ornstein-Uhlenbeck (OU) model. After this we discuss the Kalman
filter in detail, and its application with this model. After a demonstration of
the Kalman filter on a simulated OU process and a discussion of maximum
likelihood estimation (MLE) for estimating model parameters, we apply the
Kalman filter with the OU process and trailing parameter estimation to real
stock market data. We finish by proposing a simple day-trading algorithm using
the Kalman filter with the OU process and backtest its performance using
Apple's stock price. We then move to the Heston model, a combination of
Geometric Brownian Motion and the OU process. Maximum likelihood estimation is
commonly used for Heston model parameter estimation, which results in very
complex forms. Here we propose an alternative but easier way of parameter
estimation, called the method of moments (MOM). After the derivation of these
estimators, we again apply this method to real stock data to assess its
performance.