结构转换条件下利率期限结构建模及应用研究
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摘要
利率期限结构是金融理论应用研究最活跃领域之一,它是资产定价、金融产品设计、保值和风险管理、套利以及投机等的基准。随着我国债券市场的发展、金融创新的不断深入以及利率市场化进程的逐步推进,利率期限结构问题研究的重要性日益凸现。本文采用金融数学的理论和方法,从结构转换条件下利率期限结构的理论基础、静态利率期限结构拟合模型、结构转换条件下动态利率期限结构模型、结构转换条件下中国利率期限结构模型实证检验、结构转换条件下基于利率期限结构的债券期权定价等方面系统研究结构转换条件下的利率期限结构问题。
本文从理论上对利率期限结构进行分析,从收益率的角度构建利率期限结构分析的理论框架,对利率期限结构曲线的收益水平和波动性进行度量,分析了利率期限结构收益曲线的影响因素。通过结构转换的分析,结合结构转换的判断准则,然后对结构转换的阈值模型、混合模型、马尔可夫转换模型进行分析。在结构转换条件下对利率期限结构的特性分析,结合美国利率期限结构的分析,认为需要在结构转换条件下研究我国的利率期限结构,为构造结构转换条件下利率期限结构建模及应用奠定了理论基础。
文中在分析无套利假设的基础上,定义了贴现函数、即期利率和远期利率之间的数学关系。采用差商定义三次B样条函数拟合模型的贴现函数,并对贴现拟合模型的目标函数加入可变惩罚项,根据债券的剩余年限选择惩罚函数项,采用二阶微分算子法对惩罚项进行模型计算。选取上海证券交易所的国债交易数据对模型进行拟合计算,然后采用精确性和平滑性指标对模型进行了检验,结果表明该模型提高了拟合计算效率,具有较高的精确性和平滑性。
本文在考虑结构变量对经济环境的影响的基础上,分析结构转换条件下经济个体投资机会和目标函数,在单因子CHLS利率模型框架下,采用连续形式两结构马尔可夫链设置下,建立Hamilton的结构转换利率模型,将两结构马尔可夫结构转换扩展到三结构条件下,剔除了通货膨胀对利率的影响,建立三结构利率期限结构模型。在结构转换概率为时变概率时,将利率变动与过去经济信息变量结合建立动态利率期限结构模型,通过Gibbs抽样方法对参数进行估计。
本文对全国银行间同业拆借利率的月数据进行描述性统计与单位根检验后,计算Hamilton结构转换利率期限结构模型、三结构利率期限结构模型和时变概率结构转换利率期限结构模型的参数,然后分别对三个结构转换利率期限结构模型的结构个数、结构识别能力和预测能力检验,检验结果表明时变概率结构转换利率期限结构模型是适合描述我国利率动态变化的模型。
本文在结构转换条件下应用利率期限结构分析债券期权定价。从利率动态变化、结构转换和期权定价三个方面进行分析,对结构转换条件下的债券和债券期权进行定价,考虑了结构转换对利率衍生物定价的影响,利用Ito引理获得债券定价的偏微分方程,并得到债券期权定价的特征函数与递归等式。采用灵敏度分析方法研究了初始结构概率、结构持续性和结构波动率的估计值与期权价值之间的关系。
Term structure of interest rate is one of the most active research fields on finance theory and application. It is the benchmark for asset pricing, financial product design, hedging, risk management, arbitrage and speculation. With the development of financial markets, the deepening of financial innovations and the market-oriented process of interest rate, the importance of term structure research is more and more obvious in China. The dissertation employs the theory and methods of financial mathematics to study theoretical basis of term structure of interest rates with regime-switching, static term structure of interest rates fitting model, term structure of interest rates dynamic model with regime - switching, empirical China’s term structure of interest rates with regime-switching, bond option pricing with regime-switching. Combining the analysis of term structure of USA, the study shows that China’s term structure of interest rates should be analyse with regime-switching. The results settle the theory foundation for modeling and application of term structure.
Analyzing term structure of interest rate in theory, the dissertation establishes a theory framework of analysis on term structure of interest rate according yield rate, measures the level and volatility of yield curve, studies the factors of term structure of interest rate yield curve. After a characteristic analysis on regime-switching, the dissertation analizes judging criteria for regime-switching, reviews threshold model, mixture model, and Markov switching model on regime-switching.
The dissertation analyzes the assumption of non-arbitrage, and defines discount function, spot rate and forward rate. Basing on the cubic B-spline function defined by difference quotient, the model designs the weights of treasury bonds, uses the variable roughness penalty method, and estimates parameters by second-difference operator. Selecting SEE T-bonds data for fitting, testing the model by accuracy and smoothness indices, the result shows that the model improves the calculating efficiency of fitting, performances good in accuracy and smoothness.
The dissertation analyzes investment opportunity and objective function of consumer with regime-swithcing basing on the effection of state variables on the underlying economy. In the framework of CHLS interest rate model, the dissertation applies continuous two states Markov chain, develops a Hamilton interest rate model with regime-swithching, then extends the Markov regime-swithcing to three states specification, develops a three regime interest rate model without considering inflation. When regime-swithing probability is time-varying, the dissertation develops a dynamic interest rate model with combining interest rate movement with the past economy information, and estimates the parameters by Gibbs sampling.
The dissertation makes a descriptive statistics and an unit root test on the monthly weighted average interest rate of CHIBOR, estimates the parameters of Hamilton term structure of interest rate with regime-switching, three states interest rate model and interest rate model with time-varying regime-swithing probability, then test the number of regmies, regime classification measure and forcast capability of three model. The results of the test show that the interest rate model with time-varying regime-swithing probability is suitable for descripting the interest rate of China.
The dissertation analyzes the movement of interest, regime-switching and option pricing, prices the bond and bond option with regime-swithcing. Considering the regime-switching effects on interest rate derivatives pricing, the dissertation derives partial differential equation with Ito lemma, the characteristic function and recursion of bond option pricing, the relation between option value and initial regime probabilities, regime persistence, and estimated volatility.
本文从理论上对利率期限结构进行分析,从收益率的角度构建利率期限结构分析的理论框架,对利率期限结构曲线的收益水平和波动性进行度量,分析了利率期限结构收益曲线的影响因素。通过结构转换的分析,结合结构转换的判断准则,然后对结构转换的阈值模型、混合模型、马尔可夫转换模型进行分析。在结构转换条件下对利率期限结构的特性分析,结合美国利率期限结构的分析,认为需要在结构转换条件下研究我国的利率期限结构,为构造结构转换条件下利率期限结构建模及应用奠定了理论基础。
文中在分析无套利假设的基础上,定义了贴现函数、即期利率和远期利率之间的数学关系。采用差商定义三次B样条函数拟合模型的贴现函数,并对贴现拟合模型的目标函数加入可变惩罚项,根据债券的剩余年限选择惩罚函数项,采用二阶微分算子法对惩罚项进行模型计算。选取上海证券交易所的国债交易数据对模型进行拟合计算,然后采用精确性和平滑性指标对模型进行了检验,结果表明该模型提高了拟合计算效率,具有较高的精确性和平滑性。
本文在考虑结构变量对经济环境的影响的基础上,分析结构转换条件下经济个体投资机会和目标函数,在单因子CHLS利率模型框架下,采用连续形式两结构马尔可夫链设置下,建立Hamilton的结构转换利率模型,将两结构马尔可夫结构转换扩展到三结构条件下,剔除了通货膨胀对利率的影响,建立三结构利率期限结构模型。在结构转换概率为时变概率时,将利率变动与过去经济信息变量结合建立动态利率期限结构模型,通过Gibbs抽样方法对参数进行估计。
本文对全国银行间同业拆借利率的月数据进行描述性统计与单位根检验后,计算Hamilton结构转换利率期限结构模型、三结构利率期限结构模型和时变概率结构转换利率期限结构模型的参数,然后分别对三个结构转换利率期限结构模型的结构个数、结构识别能力和预测能力检验,检验结果表明时变概率结构转换利率期限结构模型是适合描述我国利率动态变化的模型。
本文在结构转换条件下应用利率期限结构分析债券期权定价。从利率动态变化、结构转换和期权定价三个方面进行分析,对结构转换条件下的债券和债券期权进行定价,考虑了结构转换对利率衍生物定价的影响,利用Ito引理获得债券定价的偏微分方程,并得到债券期权定价的特征函数与递归等式。采用灵敏度分析方法研究了初始结构概率、结构持续性和结构波动率的估计值与期权价值之间的关系。
Term structure of interest rate is one of the most active research fields on finance theory and application. It is the benchmark for asset pricing, financial product design, hedging, risk management, arbitrage and speculation. With the development of financial markets, the deepening of financial innovations and the market-oriented process of interest rate, the importance of term structure research is more and more obvious in China. The dissertation employs the theory and methods of financial mathematics to study theoretical basis of term structure of interest rates with regime-switching, static term structure of interest rates fitting model, term structure of interest rates dynamic model with regime - switching, empirical China’s term structure of interest rates with regime-switching, bond option pricing with regime-switching. Combining the analysis of term structure of USA, the study shows that China’s term structure of interest rates should be analyse with regime-switching. The results settle the theory foundation for modeling and application of term structure.
Analyzing term structure of interest rate in theory, the dissertation establishes a theory framework of analysis on term structure of interest rate according yield rate, measures the level and volatility of yield curve, studies the factors of term structure of interest rate yield curve. After a characteristic analysis on regime-switching, the dissertation analizes judging criteria for regime-switching, reviews threshold model, mixture model, and Markov switching model on regime-switching.
The dissertation analyzes the assumption of non-arbitrage, and defines discount function, spot rate and forward rate. Basing on the cubic B-spline function defined by difference quotient, the model designs the weights of treasury bonds, uses the variable roughness penalty method, and estimates parameters by second-difference operator. Selecting SEE T-bonds data for fitting, testing the model by accuracy and smoothness indices, the result shows that the model improves the calculating efficiency of fitting, performances good in accuracy and smoothness.
The dissertation analyzes investment opportunity and objective function of consumer with regime-swithcing basing on the effection of state variables on the underlying economy. In the framework of CHLS interest rate model, the dissertation applies continuous two states Markov chain, develops a Hamilton interest rate model with regime-swithching, then extends the Markov regime-swithcing to three states specification, develops a three regime interest rate model without considering inflation. When regime-swithing probability is time-varying, the dissertation develops a dynamic interest rate model with combining interest rate movement with the past economy information, and estimates the parameters by Gibbs sampling.
The dissertation makes a descriptive statistics and an unit root test on the monthly weighted average interest rate of CHIBOR, estimates the parameters of Hamilton term structure of interest rate with regime-switching, three states interest rate model and interest rate model with time-varying regime-swithing probability, then test the number of regmies, regime classification measure and forcast capability of three model. The results of the test show that the interest rate model with time-varying regime-swithing probability is suitable for descripting the interest rate of China.
The dissertation analyzes the movement of interest, regime-switching and option pricing, prices the bond and bond option with regime-swithcing. Considering the regime-switching effects on interest rate derivatives pricing, the dissertation derives partial differential equation with Ito lemma, the characteristic function and recursion of bond option pricing, the relation between option value and initial regime probabilities, regime persistence, and estimated volatility.
引文
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89郑振龙,林海.中国市场利率期限结构的静态估计.武汉金融. 2003, (3): 33~37
90朱峰.国债即期收益率曲线的拟合估计.证券市场导报. 2003, (4): 31~35
91刘灿,易璐.深沪两市国债收益率期限结构的实证研究.证券市场导报. 2004, (2): 36~40
92周子康,王宁,杨衡.中国国债利率期限结构模型研究与实证分析.金融研究. 2008, (3):131~150
93闵小平,田澎.基于B样条函数的上交所利率期限结构估计.管理工程学报. 2006, 20(4): 77~81
94傅曼丽,屠梅增,董荣杰.债券利率期限结构的构造方法与实证检验.系统工程理论方法应用. 2006, 15(5): 436~440
95何启志,何建敏,陈珊珊.利率期限结构指数样条模型实证研究.管理科学. 2008, 21(1): 100~107
96 H. Lin, Z. Zheng. Dynamic Behavior of Interest Rates in China. Chinese Business Review. 2003, (2): 1~12
97谢赤,邓艺颖.描述利率动态行为的GARCH-JUMP模型.数量经济技术经济研究. 2003, (3): 74~77
98张金青,周茂彬.中国短期利率跳跃行为的实证研究.统计研究. 2008, 25(1): 59~64
99谢赤,钟羽.关于制度转换Vasicek利率期限结构模型.科学技术与工程. 2004, 4(9): 798~803
100洪永淼,林海.中国市场利率动态研究_基于短期国债回购利率的实证分析.经济学季刊. 2006, 5(2): 511~532
101唐齐鸣,高翔.我国同业拆借市场利率期限结构的实证研究.统计研究.2002, (5): 33~36
102李彪,汤宝臣.基于国债回购市场数据的利率预期理论检验.统计与决策. 2007, (2): 108~109
103谢赤,陈晖,何源.基于理性期望的利率期限结构预期理论与期限溢酬.系统管理学报. 2008, 17(3): 283~289
104李成,马国校. VaR模型在我国银行同业拆借市场中的应用研究.金融研究. 2007, (5) : 62~77
105李玉锁,齐中英.银行间同业拆借利率的复杂性研究.管理工程学报. 2008, 22(1): 40~44.
106范龙振.债券隐含利率与多因子Vasicek模型.系统工程理论方法应用. 2004, 13(5): 455~459
107范龙振,张国庆.两因子CIR模型对上交所利率期限结构的实证研究.系统工程学报. 2005, 20(5): 447-453
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110林海,郑振龙.中国利率动态模型研究.财经问题研究. 2005, (9): 45~49
111陈晖,谢赤.中国银行间同业拆借市场利率结构转换研究.管理科学. 2004, 17(4):65~70
112李红,杨向群. CIR利率模型的期权定价.经济数学. 2007, 24(3): 244~247
113宋永安,陆立强.非参数利率期限结构动态模型及衍生品定价.复旦学报. 2008, 47(2): 213~219
114王明好,陈忠,李丽.基于跳跃_扩散利率模型的浮动利率抵押贷款支持证券定价研究.管理工程学报. 2007, 21(1): 77~82
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88林海,郑振龙.利率期限结构研究述评.管理科学学报. 2008, 10(1): 79~93
89郑振龙,林海.中国市场利率期限结构的静态估计.武汉金融. 2003, (3): 33~37
90朱峰.国债即期收益率曲线的拟合估计.证券市场导报. 2003, (4): 31~35
91刘灿,易璐.深沪两市国债收益率期限结构的实证研究.证券市场导报. 2004, (2): 36~40
92周子康,王宁,杨衡.中国国债利率期限结构模型研究与实证分析.金融研究. 2008, (3):131~150
93闵小平,田澎.基于B样条函数的上交所利率期限结构估计.管理工程学报. 2006, 20(4): 77~81
94傅曼丽,屠梅增,董荣杰.债券利率期限结构的构造方法与实证检验.系统工程理论方法应用. 2006, 15(5): 436~440
95何启志,何建敏,陈珊珊.利率期限结构指数样条模型实证研究.管理科学. 2008, 21(1): 100~107
96 H. Lin, Z. Zheng. Dynamic Behavior of Interest Rates in China. Chinese Business Review. 2003, (2): 1~12
97谢赤,邓艺颖.描述利率动态行为的GARCH-JUMP模型.数量经济技术经济研究. 2003, (3): 74~77
98张金青,周茂彬.中国短期利率跳跃行为的实证研究.统计研究. 2008, 25(1): 59~64
99谢赤,钟羽.关于制度转换Vasicek利率期限结构模型.科学技术与工程. 2004, 4(9): 798~803
100洪永淼,林海.中国市场利率动态研究_基于短期国债回购利率的实证分析.经济学季刊. 2006, 5(2): 511~532
101唐齐鸣,高翔.我国同业拆借市场利率期限结构的实证研究.统计研究.2002, (5): 33~36
102李彪,汤宝臣.基于国债回购市场数据的利率预期理论检验.统计与决策. 2007, (2): 108~109
103谢赤,陈晖,何源.基于理性期望的利率期限结构预期理论与期限溢酬.系统管理学报. 2008, 17(3): 283~289
104李成,马国校. VaR模型在我国银行同业拆借市场中的应用研究.金融研究. 2007, (5) : 62~77
105李玉锁,齐中英.银行间同业拆借利率的复杂性研究.管理工程学报. 2008, 22(1): 40~44.
106范龙振.债券隐含利率与多因子Vasicek模型.系统工程理论方法应用. 2004, 13(5): 455~459
107范龙振,张国庆.两因子CIR模型对上交所利率期限结构的实证研究.系统工程学报. 2005, 20(5): 447-453
108范龙振,张国庆.仿射模型、广义仿射模型与上交所利率期限结构.管理工程学报. 2005, 19(3): 97~101
109范龙振.短期利率模型在上交所债券市场上的实证分析.管理科学学报. 2007, 10(2): 80~89
110林海,郑振龙.中国利率动态模型研究.财经问题研究. 2005, (9): 45~49
111陈晖,谢赤.中国银行间同业拆借市场利率结构转换研究.管理科学. 2004, 17(4):65~70
112李红,杨向群. CIR利率模型的期权定价.经济数学. 2007, 24(3): 244~247
113宋永安,陆立强.非参数利率期限结构动态模型及衍生品定价.复旦学报. 2008, 47(2): 213~219
114王明好,陈忠,李丽.基于跳跃_扩散利率模型的浮动利率抵押贷款支持证券定价研究.管理工程学报. 2007, 21(1): 77~82
115石柱鲜,孙皓,邓创.中国主要宏观经济变量与利率期限结构的关系:基于VAR-ATSM模型的分析.世界经济. 2008, (3): 53~59
116郭涛,宋德勇.中国利率期限结构的货币政策含义.经济研究. 2008, (3): 39~47
117 J. Hamilton. Regime-switching Models. Palgrave Dictionary of Economics.. 2005: 1~15
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