金融资产波动率建模在现代金融工程中具有重要地位，其应用涵盖风险管理、衍生品定价和投资组合优化等核心领域。本文着重探讨三种主流波动率建模方法：广义自回归条件异方差模型(GARCH)、Glosten-Jagannathan-Runkle-GARCH模型(GJR-GARCH)以及异质自回归模型(HAR)。

预测波动率是指市场交易者对未来价格波动率做出的预测值。交易者预测时，往往通过标的资产历史价格或历史波动率进行加权平均，得出一个未来波动率的预测值。常见的预测波动率模型有EWMA模型和 GARCH模型等。 GARCH模型 自从Engle(1982)提出ARCH模型分析 ...

本篇是“学海拾珠”系列第二百二十四篇，文献旨在探讨引入量化策略估算投资组合的方差-协方差矩阵的益处，期望能够有效捕捉资产收益的典型特征，并在时变波动率的环境下，对 150 只 ETF 进行优化与再平衡。主要比较了三种模型：（a）样本协方差或等权重 ...

Will Kenton is an expert on the economy and investing laws and regulations. He previously held senior editorial roles at Investopedia and Kapitall Wire and holds a MA in Economics from The New School ...

This is the first paper that estimates the price determinants of Bitcoin in a generalized autoregressive conditional heteroscedasticity (GARCH) framework using high-frequency data. Derived from a ...

Journal of Economic Integration, Vol. 30, No. 1 (March 2015), pp. 172-205 (34 pages) In this paper, we use the copulas functions in financial application, namely to examine the assumption of ...

本综述通过马尔可夫机制转换GJR-GARCH（MS-GJR-GARCH）模型深入解析土耳其日前电力市场的价格波动机制，识别中度、高度和极端三种波动状态，并量化可再生能源（如太阳能、风能）与天然气发电对波动性的差异化影响。研究揭示了地缘政治冲突（如俄乌战争）与 ...

In Duan, Gauthier and Simonato (1999), an analytical approximation to price European options in the generalized autoregressive conditional heteroskedastic (GARCH) framework was developed. The formula ...

The asymptotic theory for the sample autocorrelations and extremes of a GARCH(1, 1) process is provided. Special attention is given to the case when the sum of the ARCH and GARCH parameters is close ...