基于GARCH模型的股票风险度量探究

基于GARCH模型的股票风险度量探究

姓 名：曹 荔 院部名称：数学学院 专 业：应用数学 研究方向：经济数学

摘 要

经过近20年的发展，我国证券市场已形成了与我国经济发展相适应的特色道路，规模不断扩大，上市公司数量不断增加，投资者积极性不断提高，制度性建设日趋完善。但股票市场在诸多方面的不完善性仍较为明显。尤其是从2008年开始的下滑行情造成了重大的负面影响、损害了投资这的利益。所以证券市场的风险度量成为金融市场管理的焦点，风险度量逐渐成为金融市场风险管理的核心，同时，这些也对风险度量提出了挑战，需要更加适合的模型方法来处理这些情况。目前，度量风险比较流行的方法是VaR方法。VaR不但可以对未来的情景进行估计，而且仅用单一数字即可表征一个组合或者一家金融机构在一段时期内所面临的市场风险。实际的资产收益分布具有尖峰后尾特征，在正态分布条件下的VaR估计将导致VaR测度产生低估风险。

基于GARCH（广义自回归条件异方差）模型是由Tim Bollerslev在ARCH模型的基础上提出来的。GARCH模型描述了股市收益率序列的自相关性，具有反映市场时变的特征，能比较好的描述金融市场的动态性和复杂性。本文分为4章来探讨GARCH模型的股票风险度量。

第1章为绪论。本章阐述了论文研究的背景、研究现状，提出了研究的问题，指出了论文研究的理论意义与实践意义，并对论文结构安排进行了说明，归纳出论文的主要创新工作。全面回顾和梳理已有的关于金融风险理论的文献基础上，本章对金融风险、金融风险管理和风险价值的计算方法进行了阐述。风险价值计算是金融风险管理的核心环节，而利用LARCH模型进行风险价值的计算是本文的研究重点。同时本文还回顾了关于风险传染的理论文献，为后来的基于多元LARCH模型的风险传染研究做好理论准备。

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第2章概述了 VaR 方法的基本原理，包括 VaR 的定义， VaR 的计算公式和一般计算步骤。 接着对 VaR 的不同基本方法进行了阐述，以及对GARCH类模型：自回归条件异方差模型(ARCH模型)，指数GARCH模型(EGARCH)，PowerARCH模型(PARCH)，均值自回归条件异方差模型(GARCH-M模型)，VaR 与GARCH类模型的用途做了详细的分析。简而言之，本章既是对 VaR 方法与GARCH类模型的讨论，为后面章节的实证分析提供理论的依据和指导。在下章中将根据本章所介绍的各种计算 VaR 的方法和GARCH类模型对我国股票市场的风险进行度量和检验。

第3章上是本文的重点，通过对上海证券交易所股票风险度量的实证分析，沪，通过刘一沪巾一段时期内的收益率序列进行检验，得到收益率残差序列满足ARCH效应，所以GARCH模型非常适合V aR计算’}’的波动性的估计。基于2种不同分布(t分布和GED分布)假定下，讨论GARCH类模型的VaR计算，并从实际数据出发计算了沪巾2005年1月31日到2009年12月31日平均一天期的VaR值，据此定量测量股票巾场风险，这可以为股票投资机构的风险管理及一般股票投资者的投资风险分析提供依据。通过对深股市市场风险度量的模型选择与比较，分别采用等权移动平均方法、指数加权移动平均方法、GARCH(1，1)方法、GARCH(1，1)-t方法和Pareto型极值分布方法计算上海和深圳股票日收益率的VaR。向后检验表明，Pareto型极值分布方法比其他方法更能准确地反映我国股市的风险。

第4章总结了基于GARCH模型，对金融资产和投资组合的风险价值计算的实证分析结果，得出了对于金融资产风险价值度量的最佳模型设定，并对基于多元GARCH模型的金融资产的波动传染机制进行了分析，在对 VaR 探讨的过程提出了有很多的不足之处，以待后续研究。

关键词：VaR GARCH模型 股票风险 度量

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Abstract

After almost 20 years of development, our country securities market has already formed with China's economic development to adapt the characteristics of road, scale unceasingly expands, the listed company increasing of quantity, investor enthusiasm unceasing enhancement, institutional construction increasing perfection. But stock market in many aspects of faultiness remained relatively obvious. Especially since the start of 2008 decline of market caused a great negative impact, harm the interests of the investment. So of the securities market risk metric become the focus of the financial market management, risk metric gradually become the core of financial market risk management, and at the same time, these also poses a challenge to risk measurement, need more suitable model methods to deal with these situations. At present, a measure of risk more popular method is VaR method. VaR can not only for the future situation of estimation, and only with a single figures can be characterized a combination or a financial institution in a period of facing the market risk. Actual assets income distribution has rush yixiang characteristic, in normal distribution under the condition of the VaR estimate will lead to produce underestimated risk measurement VaR.

Based on GARCH (generalized auto-regressive conditional heteroscedastic) model was established by Tim Bollerslev in the ARCH model based on carry out. GARCH model describes the stock market returns sequence between autocorrelation, have reflect market time-varying characteristics, can better description of financial market dynamics and complexity. This paper will be divided into 4 chapter GARCH model to explore the stock risk measurement.

Chapter 1 for introduction. This chapter expounds the research background, research situation, this paper proposes the research question, points out the dissertation research theoretical significance and

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practical significance, and the paper the structure arrangement, illustrates the paper concludes the main innovation work. A comprehensive review and combed the existing financial risk theory about the literature basis, this chapter for financial risk, financial risk management and risk value calculation method is discussed in this paper. Risk JiaZhiJi is financial risk management of the key sectors, and the use of LARCH model risk value computation in this paper is discussed. The paper also reviewed the literatures about risk contagion theory, for the later based on multivariate LARCH model of risk contagion research do theories preparation.

Chapter 2 summarizes VaR method, the basic principle of including VaR definition, VaR calculation formula of and general calculation steps. Then the different basic method for VaR is discussed, and the GARCH kinds of models: auto-regressive conditional heteroscedastic model (the ARCH model), index GARCH model (EGARCH), PowerARCH model (PARCH), mean auto-regressive conditional heteroscedastic model (garch-m model), with such GARCH model VaR USES to do a detailed analysis. In short, this chapter is VaR method and GARCH kinds of models of discussion, the empirical analysis for later chapter provide theoretical basis and guidance. In the next chapter will according to this chapter introduces various calculation VaR method and GARCH class model on Chinese stock market risk measurement and test.

Chapter 3 is this paper focuses on the Shanghai stock exchange, through to the stock risk measure empirical analysis, Shanghai, through that Shanghai towel for a period of time in the sequence of yield of the inspection, get yields residual sequence satisfy the ARCH effect GARCH model, so very suitable for V aR calculation '} 'volatility estimates. Based on two different distribution (t distribution and GED distribution) assumption that GARCH class discussion the VaR model, and the calculation based on actual data calculated from Shanghai towel in January 2005 31 to December 31, 2009 average day period VaR value, accordingly quantitative measure fabric field risk, the stock for stock investment the

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