长记忆波动率的模型研究与实证分析

发布时间：2018-05-03 23:03

本文选题：长记忆性 + 高频数据　；参考：《西北农林科技大学》2013年硕士论文

【摘要】：近半个世纪以来，中国的经济形式呈现出了前所未有的发展势态，尤其值得关注的是自2001年中国正式成为WTO成员国以来，面对复杂多变的世界经济形势，中国的经济将不可避免的受到来自外界环境的各种挑战，而作为经济发展命脉的金融市场的发展已经成为经济领域的研究者和管理者关注的焦点。在金融领域里关于各种金融资产价格波动的研究一直是众多经济研究者关注的焦点之一，特别是计算机技术的迅猛发展，极大地方便了各种金融数据的获取和存储，使得高频甚至超高频数据的获取和存储成为了现实。经典的波动率模型主要是以频率较低的数据如日、星期、月为建模研究的对象，不仅数据量小，而且获取周期比较长，而利用金融高频数据进行建模研究，就可以在很短的时间段内获得大量的数据，大大的缩短了数据的获取周期，从而也就节省了大量时间。和低频数据相比较，高频数据则体现出更加丰富的价格变动过程中的信息和长期日间现象的信息，这将大大有利于市场中某些微观结构理论的研究。所以，与传统的建立在低频数据基础上的波动率建模研究的不同，本文主要是在上证5间隔的高频数据的基础上研究波动率及其长记忆性。自从Engle（1951）发现时间序列的长记忆性这一性质以来，对长记忆这一性质的建模和分析正日益受到金融界的广泛关注，因为长记忆性就意味着现在的状态将持续影响将来，这对于金融风险管理有着不可忽视的作用。本文研究了两个非常重要的长记忆时间序列模型：分数差分噪声（FDN）模型和分整自回归移动平均ARFIMA模型，还对已实现波动率的ARFIMA-RV模型进行了研究。自从已实现波动率被提出后，张世英等学者对其进行了扩展和改进，得到了赋权已实现波动率，查阅大量文献资料，发现目前对于赋权已实现波动率的建模研究鲜有涉及，尽管众多学者认为ARFIMA模型已经能够很好的预测波动率，但是如何把赋权已实现波动率和ARFIMA有效的结合起来，从而建议一个符合高频数据自身性质同时也可以用来估计市场波动率的模型是目前关于波动率建模中一个比较新的研究方向和难点，本文所做的研究就是在这一问题背景下展开的。通过实证分析，得出了赋权已实现波动率存在长记忆性，并且对赋权已实现波动率取对数后，得到的序列表现出了非常明显的正态性的特征，，基于此特点和其长记忆性建立了对数赋权已实现波动率的分整自回归移动平均模型（ARFIMA-ARIMA-lnWRV），通过参数估计确定了模型中各参数的值，同时对结果进行了检验，证实了模型的良好性，最后介绍了VaR模型的发展及应用，并研究了赋权已实现波动率在风险价值度量VaR中的应用。
[Abstract]:In the past half century, China's economic form has taken on an unprecedented development, especially since China became a member of the WTO in 2001, facing the complex and changeable world economic situation. China's economy will inevitably be challenged by the external environment, and the development of the financial market, which is the lifeblood of economic development, has become the focus of attention of researchers and managers in the economic field. In the field of finance, the research on the fluctuation of the price of various kinds of financial assets has been one of the focuses of many economic researchers, especially the rapid development of computer technology, which greatly facilitates the acquisition and storage of all kinds of financial data. It makes the acquisition and storage of high frequency and even ultra high frequency data become a reality. The classical volatility model is mainly based on low-frequency data such as day, week and month. It not only has a small amount of data, but also has a long acquisition period. It can obtain a lot of data in a very short period of time, greatly shorten the period of data acquisition, and thus save a lot of time. Compared with the low-frequency data, the high-frequency data reflect more abundant information in the process of price change and the information of long-term daytime phenomenon, which will greatly benefit the study of some microstructural theories in the market. Therefore, unlike the traditional research on volatility modeling based on low frequency data, this paper mainly studies volatility and its long memory on the basis of high frequency data of 5 interval in Shanghai Stock Exchange. Since Engle discovered the property of long memory in time series, the modeling and analysis of long memory has attracted more and more attention in the financial world, because long memory means that the present state will continue to affect the future. This for financial risk management has a role that can not be ignored. In this paper, two very important long memory time series models: fractional differential noise (FDN) model and fractional autoregressive moving average (ARFIMA) model are studied. The ARFIMA-RV model of realized volatility is also studied. Since the realization of volatility has been put forward, Zhang Shiying and other scholars have extended and improved it, obtained weighted realized volatility, consulted a lot of literature, found that the modeling of weighted realized volatility is rarely involved. Although many scholars think that ARFIMA model has been able to predict volatility, but how to effectively combine weighted realized volatility with ARFIMA. Therefore, it is suggested that a model which can also be used to estimate market volatility in accordance with the nature of high frequency data is a relatively new research direction and difficulty in volatility modeling. The research done in this paper is carried out under the background of this problem. Through the empirical analysis, it is concluded that the weighted realized volatility has long memory, and the logarithm of the weighted realized volatility shows the characteristic of normality. Based on this characteristic and its long memory property, an ARFIMA-ARIMA-lnWRVV model of integral autoregressive moving average (ARFIMA-ARIMA-lnWRVV) with logarithmic weighting of realized volatility is established. The values of each parameter in the model are determined by parameter estimation, and the results are verified and the model is proved to be good. Finally, the development and application of VaR model are introduced, and the application of weighted realized volatility in VaR is studied.
【学位授予单位】：西北农林科技大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F832.5

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