结构转换模型及其在长期风险管理中的应用
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摘要
次贷危机在全球金融市场的肆虐引发了人们对金融衍生产品及风险管理的重新思考和进一步重视。虽然金融创新产品能够成为风险重构、风险分散、风险对冲的工具,解决资金流动的瓶颈,降低资金使用成本,拓宽融资渠道,增加市场活力,但是,在金融机构对高额利润的过分追求以及对经济、金融环境发展趋势缺乏远见的情况下,金融创新产品自身的杠杆作用会使风险放大并加速传播。
本文以长期风险管理为切入点,引入在长跨期时间序列数据建模中较为流行的,具有灵活性和非线性特征的模型——马尔科夫结构转换模型。在国外,它很早就被用于分析GNP等宏观经济数据,以捕捉经济系统里偶然但重复出现的结构变化。近年来,它也被用来度量股票、债券等金融产品的市场风险,并成为保险公司等关注长期投资风险的机构推荐使用的风险准备金计算模型。而国内对它的研究多限于实证方面,未有更深入的探讨和创新。
本文由六个章节组成。
第一章简述风险管理的发展与重要性,综述国内外结构转换模型的研究成果,并提出全文架构。
第二章从结构转换模型的构造原理出发,详细介绍了模型设定、参数估计方法、残差分析以及对普通结构转换模型性进行扩展的思路。
第三章应用结构转换模型分析信用风险。对反映市场信用风险水平的CDS指数建立结构转换模型,将其分为信用利差缩小、波动减弱状态和利差扩大、波动增加状态,分析CDS指数对金融市场事件的反应。同时,在以其为标的资产的标准化CDO权益级分券的定价中加入经济周期、行业周期等长期风险因素,预测在信用风险激增的危机时期CDO价格的变化趋势。
第四章再次回到股票市场分析中。首先,考察了结构转换模型对股票市场长期收益率分布尖峰、厚尾、偏斜特征的描述,并通过比较它与其他模型估计的股市下跌概率,证明其在预计市场下泄风险上的准确性。其次,利用结构转换模型对样本时间序列敏感的特点,根据参数估计值的变化,设计出检测股票价格序列变点的方法。通过对美国股市的实证分析证明变点检测方法的有效性。
第五章创新性的提出带约束的结构转换模型CRSLN。其通过在转移矩阵中加入约束条件来引入均值回复效应,既对样本时间序列的选择不过份敏感,也较好的缓解了一般均值回复模型对尾部风险的低估。最后,基于CRSLN模型描述的股指动态过程,对股指期权的定价提出初步的构思。
最后一章是对全文的总结,指出文中亟待改进之处以及未来研究方向。
The outbreak of subprime mortgage crisis leads the world to reconsider about the financial derivatives trading and the importance of risk management. The innovation of financial products may be useful for reconstructing risk distribution, diversifying the risk and hedging the risk. At the meantime, it will help financial institution to break through the limitation of liquidity, to reduce financing cost, and then, to bring us a dynamic market. However, if market participants pay more attention to profit maximization, without noticing or foreseeing the long-term trend or changes of economic and financial environment, the leverage of derivatives will enlarge the risks and bring them to worldwide.
Based on the necessity of long-term risk management, we focus on a popular nonlinear time series model, Markov regime-switching model. It is very flexible and widely used in analyzing long-run dynamics of macro economy, like GNP data, to capture those unexpected but recurrent phenomena. Recently, it's recommended by the investors, such as insurance company, which make long-term investments, to calculate reserve. But it has not been systematically studied by domestic researchers.
The frame and innovation are described in six chapters in this paper.
In Chapter 1, the development and the importance of risk management are briefly summarized, and the researches of regime-switching models are reviewed. Then, the frame of the whole paper is introduced.
In Chapter 2, the basic theory of regime-switching type models is described. The methods to set a concrete model, estimate parameters and analyze estimation residuals are systematically presented. At last, two specific extensions of regime-switching model are listed.
Chapter 3 is the application of regime-switching model to a new field. The model is used to measure the credit risk implied by credit default swap index. We assume that the spread of CDS index locates in one of the two states, which are spread tighten-volatility decrease state and spread widen-volatility increase state. The results show that CDS index does sensitively respond to big events in financial market. Therefore, when pricing and hedging the equity tranche of standard CDO, the regime shifts of underlying CDS index and the long-run risk of economic cycle and business cycle should be considered, especially when the credit risk increases sharply in crisis period.
In Chapter 4, the research goes back to focus on stock market. Firstly, the capability of regime-switching model to represent the characteristics of asset return distribution, including high kurtosis, heavy tail and skewness, is studied and compared to other models. The result suggests that the regime-switching model forecasts the probability of downward stock market, especially the large crash, better than other models. Secondly, a change point detecting algorithm is proposed due to the sensitivity of regime-switching parameters to new information. Then the stock market is dived into bear market phase and bull market phase. The segmented regime-switching model is estimated in the whole series segmented by estimated change points. We can find that the segmented estimations are consistent with real market scene.
In Chapter 5, the constrained regime-switching model is proposed for the first time to imbed mean-reversion without underestimating the high-order moments and the tail risk. Meanwhile, the parameter estimations of CRSLN model are more robust than other two regime-switching type models. Then the stock index path modeled by the CRSLN model is used to pricing stock index option, although it is only a primary design.
The last chapter is the conclusion of the whole thesis, the shortcomings and future improvements are pointed out.
本文以长期风险管理为切入点,引入在长跨期时间序列数据建模中较为流行的,具有灵活性和非线性特征的模型——马尔科夫结构转换模型。在国外,它很早就被用于分析GNP等宏观经济数据,以捕捉经济系统里偶然但重复出现的结构变化。近年来,它也被用来度量股票、债券等金融产品的市场风险,并成为保险公司等关注长期投资风险的机构推荐使用的风险准备金计算模型。而国内对它的研究多限于实证方面,未有更深入的探讨和创新。
本文由六个章节组成。
第一章简述风险管理的发展与重要性,综述国内外结构转换模型的研究成果,并提出全文架构。
第二章从结构转换模型的构造原理出发,详细介绍了模型设定、参数估计方法、残差分析以及对普通结构转换模型性进行扩展的思路。
第三章应用结构转换模型分析信用风险。对反映市场信用风险水平的CDS指数建立结构转换模型,将其分为信用利差缩小、波动减弱状态和利差扩大、波动增加状态,分析CDS指数对金融市场事件的反应。同时,在以其为标的资产的标准化CDO权益级分券的定价中加入经济周期、行业周期等长期风险因素,预测在信用风险激增的危机时期CDO价格的变化趋势。
第四章再次回到股票市场分析中。首先,考察了结构转换模型对股票市场长期收益率分布尖峰、厚尾、偏斜特征的描述,并通过比较它与其他模型估计的股市下跌概率,证明其在预计市场下泄风险上的准确性。其次,利用结构转换模型对样本时间序列敏感的特点,根据参数估计值的变化,设计出检测股票价格序列变点的方法。通过对美国股市的实证分析证明变点检测方法的有效性。
第五章创新性的提出带约束的结构转换模型CRSLN。其通过在转移矩阵中加入约束条件来引入均值回复效应,既对样本时间序列的选择不过份敏感,也较好的缓解了一般均值回复模型对尾部风险的低估。最后,基于CRSLN模型描述的股指动态过程,对股指期权的定价提出初步的构思。
最后一章是对全文的总结,指出文中亟待改进之处以及未来研究方向。
The outbreak of subprime mortgage crisis leads the world to reconsider about the financial derivatives trading and the importance of risk management. The innovation of financial products may be useful for reconstructing risk distribution, diversifying the risk and hedging the risk. At the meantime, it will help financial institution to break through the limitation of liquidity, to reduce financing cost, and then, to bring us a dynamic market. However, if market participants pay more attention to profit maximization, without noticing or foreseeing the long-term trend or changes of economic and financial environment, the leverage of derivatives will enlarge the risks and bring them to worldwide.
Based on the necessity of long-term risk management, we focus on a popular nonlinear time series model, Markov regime-switching model. It is very flexible and widely used in analyzing long-run dynamics of macro economy, like GNP data, to capture those unexpected but recurrent phenomena. Recently, it's recommended by the investors, such as insurance company, which make long-term investments, to calculate reserve. But it has not been systematically studied by domestic researchers.
The frame and innovation are described in six chapters in this paper.
In Chapter 1, the development and the importance of risk management are briefly summarized, and the researches of regime-switching models are reviewed. Then, the frame of the whole paper is introduced.
In Chapter 2, the basic theory of regime-switching type models is described. The methods to set a concrete model, estimate parameters and analyze estimation residuals are systematically presented. At last, two specific extensions of regime-switching model are listed.
Chapter 3 is the application of regime-switching model to a new field. The model is used to measure the credit risk implied by credit default swap index. We assume that the spread of CDS index locates in one of the two states, which are spread tighten-volatility decrease state and spread widen-volatility increase state. The results show that CDS index does sensitively respond to big events in financial market. Therefore, when pricing and hedging the equity tranche of standard CDO, the regime shifts of underlying CDS index and the long-run risk of economic cycle and business cycle should be considered, especially when the credit risk increases sharply in crisis period.
In Chapter 4, the research goes back to focus on stock market. Firstly, the capability of regime-switching model to represent the characteristics of asset return distribution, including high kurtosis, heavy tail and skewness, is studied and compared to other models. The result suggests that the regime-switching model forecasts the probability of downward stock market, especially the large crash, better than other models. Secondly, a change point detecting algorithm is proposed due to the sensitivity of regime-switching parameters to new information. Then the stock market is dived into bear market phase and bull market phase. The segmented regime-switching model is estimated in the whole series segmented by estimated change points. We can find that the segmented estimations are consistent with real market scene.
In Chapter 5, the constrained regime-switching model is proposed for the first time to imbed mean-reversion without underestimating the high-order moments and the tail risk. Meanwhile, the parameter estimations of CRSLN model are more robust than other two regime-switching type models. Then the stock index path modeled by the CRSLN model is used to pricing stock index option, although it is only a primary design.
The last chapter is the conclusion of the whole thesis, the shortcomings and future improvements are pointed out.
引文
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