基于隐马尔科夫模型的波动率预测
发布时间：2018-08-02 15:17
【摘要】：从现代金融的数量化研究进程中可以发现，波动性始终是金融理论的核心问题，因此，如何对市场的波动性进行准确的度量和预测，，成为理论界和实务界所关注的焦点。现代经济计量学方法论的发展，为波动性的建模分析提供了坚实的方法论基础，随着研究的深入，在众多专家和学者的努力下，波动率模型的研究取得了显著进展。近几年发展起来的基于隐马尔科夫模型(HMM)预测波动率的方法尤其有效。 本文采用的隐马尔科夫模型由两部分组成，马尔科夫链和一般随机过程，并且可以用状态空间模型的形式来表示。其中，马尔科夫链用来描述不可观测的状态，在状态空间模型中用状态方程表示；一般随机过程用来描述观察值与不可观测的状态之间的关系，本文中将收益率作为观察值，用状态空间模型中的量测方程来刻画。一般来讲，隐马尔科夫模型的参数会随着马尔科夫链状态的增加而迅速增加[1]，这样当状态数较多时，参数估计就成为非常复杂的问题，为此，本文使用一种特殊的参数化过程，即能很好的反应波动率的市场特征，又使参数个数与马尔科夫链状态数无关。 本文应用隐马尔科夫模型预测波动率时，波动率由不可观测的马尔科夫过程驱动，观察值为收益率。通过历史行情数据得到参数估计，进而利用参数和当前的观察值，预测未来的波动率。为了验证模型的有效性，我们将预测结果与实际情况作比较，并引入GARCH模型和T-GARCH模型作为比较模型。实证结果表明了隐马尔科夫模型预测的有效性。
[Abstract]:From the quantitative research process of modern finance, it can be found that volatility is always the core problem of financial theory. Therefore, how to accurately measure and predict the volatility of the market has become the focus of attention of the theoretical and practical circles. The development of modern econometric methodology provides a solid methodological basis for the modeling and analysis of volatility. With the development of research, with the efforts of many experts and scholars, the research of volatility model has made remarkable progress. The method based on Hidden Markov Model (HMM) developed in recent years to predict volatility is particularly effective. The hidden Markov model in this paper is composed of two parts, Markov chain and general stochastic process, and can be expressed in the form of state space model. The Markov chain is used to describe the unobservable state, and the state equation is used in the state space model, and the general stochastic process is used to describe the relationship between the observed value and the unobservable state. In this paper, the rate of return is regarded as the observed value. The measurement equation in the state space model is used to describe it. In general, the parameters of Hidden Markov Model will increase rapidly with the increase of Markov chain state, so when the number of states is more, parameter estimation becomes a very complex problem. Therefore, a special parameterization process is used in this paper. Not only the market characteristics of volatility can be well reflected, but also the number of parameters is independent of the number of Markov chain states. In this paper, when using hidden Markov model to predict volatility, volatility is driven by an unobservable Markov process, and the observed value is a return rate. The parameters are estimated by historical market data, and then the future volatility is predicted by using the parameters and current observation values. In order to verify the validity of the model, we compare the prediction results with the actual situation, and introduce GARCH model and T-GARCH model as comparison models. The empirical results show that the hidden Markov model is effective.
【学位授予单位】：华南理工大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830
本文编号：2159846
[Abstract]:From the quantitative research process of modern finance, it can be found that volatility is always the core problem of financial theory. Therefore, how to accurately measure and predict the volatility of the market has become the focus of attention of the theoretical and practical circles. The development of modern econometric methodology provides a solid methodological basis for the modeling and analysis of volatility. With the development of research, with the efforts of many experts and scholars, the research of volatility model has made remarkable progress. The method based on Hidden Markov Model (HMM) developed in recent years to predict volatility is particularly effective. The hidden Markov model in this paper is composed of two parts, Markov chain and general stochastic process, and can be expressed in the form of state space model. The Markov chain is used to describe the unobservable state, and the state equation is used in the state space model, and the general stochastic process is used to describe the relationship between the observed value and the unobservable state. In this paper, the rate of return is regarded as the observed value. The measurement equation in the state space model is used to describe it. In general, the parameters of Hidden Markov Model will increase rapidly with the increase of Markov chain state, so when the number of states is more, parameter estimation becomes a very complex problem. Therefore, a special parameterization process is used in this paper. Not only the market characteristics of volatility can be well reflected, but also the number of parameters is independent of the number of Markov chain states. In this paper, when using hidden Markov model to predict volatility, volatility is driven by an unobservable Markov process, and the observed value is a return rate. The parameters are estimated by historical market data, and then the future volatility is predicted by using the parameters and current observation values. In order to verify the validity of the model, we compare the prediction results with the actual situation, and introduce GARCH model and T-GARCH model as comparison models. The empirical results show that the hidden Markov model is effective.
【学位授予单位】：华南理工大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830
【引证文献】
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相关硕士学位论文 前2条
1 戴晓婧;光纤通信接入技术的研究与应用[D];北京化工大学;2013年
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本文编号：2159846
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