基于波动模型的中国利率动态过程实证研究
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摘要
利率是金融市场最重要、最基础的价格变量之一。它是固定收益产品定价的基础,是投资者在衡量投资回报时候的参考指标,同时它也是宏观经济分析的重要参数。可以看出,利率对于宏观经济运行和微观金融分析而言非常重要。近年来,随着我国利率市场化改革的逐步深化,国内对利率动态过程的研究成果也越来越多。
由于金融时间序列的波动率通常具有时变的特征,因此,本文在利率单因子模型CKLS模型的基础上引入随机波动模型(SV模型)和广义自回归条件异方差模型(GARCH模型)来刻画利率波动率的动态过程。本文还对传统SV模型和GARCH模型进行了拓展,引入了跳跃因子、非正态分布等来检验我国的利率是否存在跳跃、尖峰厚尾、水平效应、均值回归等现象。
本文利用马尔可夫链蒙特卡罗模拟方法(MCMC方法)同时对SV模型、GARCH模型和CKLS模型进行估计,并利用误差信息准则——DIC准则来进行模型优劣比较。这两类波动模型的比较在国外一直存在着争议,没有形成一致的比较方法,本文中使用的方法为这两类模型的比较提供了一个新的途径。文中将MCMC方法引入基于SV模型的利率动态过程的估计,并利用MCMC方法和DIC准则来比较两类波动模型,这两个方面都是国内研究中还未涉及的领域。
本文利用WinBUGS软件完成了参数估计和模型比较。实证结果表明,用SV模型来估计我国利率动态过程的效果比GARCH模型和CKLS模型好;我国的利率动态过程表现出均值回归、水平效应、波动聚类效应等现象。本文最后还利用估计出来的各个模型进行债券定价模拟,以检验优劣程度不同的模型在进行产品定价上是否会产生差异。
Interest rate is one of the most important and fundamental parameters in financial market. It plays a fundamental role in asset pricing, risk management and macro-economy analysis. As for the importance of interest rate, a lot of literature has been devoted to the studies of interest rate and its dynamic process. There are few researches on Chinese interest rate earlier, but as the interest rate gradually liberalizes in China, the research about Chinese interest rate will become more and more.
Usually the volatility of financial time series is time-varying, so volatility models are introduced to one-factor CKLS model in this paper. These volatility models include stochastic volatility model (SV model) and GARCH model. Level effect, jump factor and non-normal distribution are also introduced to the traditional volatility models to capture the level effect, jump process, fat tail and mean-reverting effects in Chinese short rates.
This paper employs Markov Chain Monte Carlo (MCMC) method to estimate SV model, GARCH model and CKLS model and compares their performance in modeling Chinese repo rates using deviance information creteria. The comparison method between SV model and GARCH model is not consolidated and this paper applies a brand-new way. The way the paper estimates SV model and compares these models is not involved in domestic research, which makes an improvement.
This paper applies WinBUGS to complete parameter estimating and model comparison. The empirical results show that SV model is better at capturing Chinese repo rates than GARCH model and CKLS model. This result is quite robust when level effect, jump and non-normal errors are also introduced into the model. This has strong implications for asset pricing and risk management. This paper also suggest that mean-reverting, level effect and volatility clustering are significant for Chinese short rates. Finally, this paper simulates bond pricing to test whether different types of models would show significantly different results in asset-pricing.
由于金融时间序列的波动率通常具有时变的特征,因此,本文在利率单因子模型CKLS模型的基础上引入随机波动模型(SV模型)和广义自回归条件异方差模型(GARCH模型)来刻画利率波动率的动态过程。本文还对传统SV模型和GARCH模型进行了拓展,引入了跳跃因子、非正态分布等来检验我国的利率是否存在跳跃、尖峰厚尾、水平效应、均值回归等现象。
本文利用马尔可夫链蒙特卡罗模拟方法(MCMC方法)同时对SV模型、GARCH模型和CKLS模型进行估计,并利用误差信息准则——DIC准则来进行模型优劣比较。这两类波动模型的比较在国外一直存在着争议,没有形成一致的比较方法,本文中使用的方法为这两类模型的比较提供了一个新的途径。文中将MCMC方法引入基于SV模型的利率动态过程的估计,并利用MCMC方法和DIC准则来比较两类波动模型,这两个方面都是国内研究中还未涉及的领域。
本文利用WinBUGS软件完成了参数估计和模型比较。实证结果表明,用SV模型来估计我国利率动态过程的效果比GARCH模型和CKLS模型好;我国的利率动态过程表现出均值回归、水平效应、波动聚类效应等现象。本文最后还利用估计出来的各个模型进行债券定价模拟,以检验优劣程度不同的模型在进行产品定价上是否会产生差异。
Interest rate is one of the most important and fundamental parameters in financial market. It plays a fundamental role in asset pricing, risk management and macro-economy analysis. As for the importance of interest rate, a lot of literature has been devoted to the studies of interest rate and its dynamic process. There are few researches on Chinese interest rate earlier, but as the interest rate gradually liberalizes in China, the research about Chinese interest rate will become more and more.
Usually the volatility of financial time series is time-varying, so volatility models are introduced to one-factor CKLS model in this paper. These volatility models include stochastic volatility model (SV model) and GARCH model. Level effect, jump factor and non-normal distribution are also introduced to the traditional volatility models to capture the level effect, jump process, fat tail and mean-reverting effects in Chinese short rates.
This paper employs Markov Chain Monte Carlo (MCMC) method to estimate SV model, GARCH model and CKLS model and compares their performance in modeling Chinese repo rates using deviance information creteria. The comparison method between SV model and GARCH model is not consolidated and this paper applies a brand-new way. The way the paper estimates SV model and compares these models is not involved in domestic research, which makes an improvement.
This paper applies WinBUGS to complete parameter estimating and model comparison. The empirical results show that SV model is better at capturing Chinese repo rates than GARCH model and CKLS model. This result is quite robust when level effect, jump and non-normal errors are also introduced into the model. This has strong implications for asset pricing and risk management. This paper also suggest that mean-reverting, level effect and volatility clustering are significant for Chinese short rates. Finally, this paper simulates bond pricing to test whether different types of models would show significantly different results in asset-pricing.
引文
[1]Merton,Robert C..Theory of Rational Option Pricing[J].The Bell Journal of Economics and Management Science,1973,4(1):141-183.
[2]Vasicek,O..An Equilibrium Characterization of the Term Structure[J].Journal of Financial Economics,1977,5(2):177-188.
[3]Cox,John C.,Jonathan E.Ingersoll,Stephen A.Ross.A Theory of the Term Structure of Interest Rates[J].Econometrica,1985,53(2):385-407.
[4]Chan,K.C.,G.A.Karolyi,F.A.Longstaff,et al..An Empirical Comparison of Alternative Models of the Short-Term Interest Rate[J].The Journal of Finance,1992,47(3):1209-1227.
[5]Brenner,R.J.,Richard H.Harjes,Kenneth F.Kroner.Another Look at Models of the Short-Term Interest Rate[J].The Journal of Financial and Quantitative Analysis,1996,31.(1):85-107.
[6]Bali,Turan G..Modeling the Stochastic Behavior of Short-Term Interest Rates:Pricing Implications for Discount Bonds[J].Journal of Banking and Finance,2003,27(2):201-228.
[7]Das,Sanjiv R..The Surprise Element:Jumps in Interest Rates[J].Journal of Econometrics,2002,106(1):27-65.
[8]Andersen,T.G.,J.Lund.Estimating Continuous-Time Stochastic Volatility Models of the Short-Term Interest Rate[J].Journal of Econometrics,1997,77(2):343-377.
[9]Ball,Clifford A.,Walter N.Torous.The Stochastic Volatility of Short-Term Interest Rates:Some International Evidence[J].The Journal of Finance,1999,54(6):2339-2359.
[10]谢赤,邓艺颖.基于扩散模型的银行间债券市场回购利率动态的实证分析[J].系统工程,2003,21(4):90-94.
[11]傅曼丽,董荣杰,屠梅曾.动态利率模型估计方法的一个实证检验[J].华中科技大学学报:自然科学版,2005,33(4):97-100.
[12]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[J].经济学,2006,5(2):511-532.
[13]林海,郑振龙.利率期限结构研究述评[J].管理科学学报,2007,10(1):79-93.
[14]高驰,郭艳红,于英琦.中国市场短期利率动态研究-基于有效矩方法的实证分析[J].南方经济,2007,4:45-55.
[15]Clark,P.K..A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices[J].Econometrica,1973,41(1):135-156.
[16]Tauchen,G.,M.Pitts.The Price Variability-Volume Relationship on Speculative Markets[J].Econometrica,1983,51(2):485-505.
[17]Gallant,A.R.,D.Hsieh,G.Tauchen.On Fitting a Recalcitrant Series:The Pound/Dollar Exchange Rate,1974-1983[J].Nonparametric and Semiparametric Methods in Econometrics and Statistics:Proceedings of the Fifth Intemational Symposium in Economic Theory and Econometrics,Cambridge University Press,1991.
[18]朱慧明,李峰,杨锦明.基于MCMC模拟的贝叶斯厚尾金融随机波动模型分析[J].运筹与管理,2007,16(4):111-115.
[19]周彦,张世英,张彤.跳跃连续时间SV模型建模及实证研究[J].系统管理学报,2007,16(5):531-536.
[20]李传乐,王美今.SV模型的模拟GMM方法——兼论涨跌停板制度的有效性[J].中山大学学报(自然科学版),2006,45(6):11-15.
[21]余素红,张世英.SV与GARCH模型对金融时间序列刻画能力的比较研究[J].系统工程,2002,20(5):28-33.
[22]孟利锋.随机波动模型及其建模方法研究[D].天津:天津大学,2004.
[23]Harvey,A.C.,E.Ruiz,N.Shephard.Multivariate Stochastic Variance Models[J].Review of Economic Studies,1994,61(2):247-264.
[24]Melino,A.,S.M.Tumbull.Pricing Foreign Currency Options with Stochastic Volatility[J].Journal of Econometrics,1990,45(1):239-265.
[25]Sorensen,M..Prediction Based Estimating Equations[J].Econometrics,2000,3:123-147.
[26]Gallant,A.R.,D.Hsie,G.Tauchen.Estimation of Stochastic Volatility Models with Diagnostics[J].Journal of Econometrics,1997,81(1):159-192.
[27]Sandmann,G.,S.J.Koopman.Estimation of Stochastic Volatility Models via Monte Carlo Maximum Likelihood[J].Journal of Econometrics,1998,87(2):271-301.
[28]Danielsson,J..Stochastic Volatility in Asset Prices:Estimation with Simulated Maximum Likelihood[J].Journal of Econometric s,1994,64(1):375-400.
[29]Jacquier,E.,Nicholas G.Poison,Peter E.Rossi.Bayesian Analysis of Stochastic Volatility Models[J].Journal of Business & Economic Statistics,1994,12(4):371-389.
[30]Shephard,N.,M.K.Pitt.Likelihood Analysis of Non-Gaussian Measurement Time Series[J].Biometrika,1997,84(3):653-667.
[31]Kim,S.,N.Shephard,S.Chib.Stochastic Volatility:Likelihood Inference and Comparison with ARCH Models[J].Review of Economic Studies,1998,65(3):361-393.
[32]Meyer,R.,Jun Yu.BUGS for a Bayesian Analysis of Stochastic Volatility Models[J].The Econometrics Journal,2000,3(2):198-215.
[33]张世英,樊智.协整理论与波动模型[M].北京:清华大学出版社,2004.
[34]Spiegelhalter,et al..Bayesian Measures of Model Complexity and Fit[J].Journal of the Royal Statistical Society,Series B(Statistical Methodology),2002,64(4):583-639.
[35]高占军.SHIBOR负重前行[EB/OL].http://www.caijing.com.cn/investor/zqsc/2007-01-24/15966.shtml,2007-1-24.
[2]Vasicek,O..An Equilibrium Characterization of the Term Structure[J].Journal of Financial Economics,1977,5(2):177-188.
[3]Cox,John C.,Jonathan E.Ingersoll,Stephen A.Ross.A Theory of the Term Structure of Interest Rates[J].Econometrica,1985,53(2):385-407.
[4]Chan,K.C.,G.A.Karolyi,F.A.Longstaff,et al..An Empirical Comparison of Alternative Models of the Short-Term Interest Rate[J].The Journal of Finance,1992,47(3):1209-1227.
[5]Brenner,R.J.,Richard H.Harjes,Kenneth F.Kroner.Another Look at Models of the Short-Term Interest Rate[J].The Journal of Financial and Quantitative Analysis,1996,31.(1):85-107.
[6]Bali,Turan G..Modeling the Stochastic Behavior of Short-Term Interest Rates:Pricing Implications for Discount Bonds[J].Journal of Banking and Finance,2003,27(2):201-228.
[7]Das,Sanjiv R..The Surprise Element:Jumps in Interest Rates[J].Journal of Econometrics,2002,106(1):27-65.
[8]Andersen,T.G.,J.Lund.Estimating Continuous-Time Stochastic Volatility Models of the Short-Term Interest Rate[J].Journal of Econometrics,1997,77(2):343-377.
[9]Ball,Clifford A.,Walter N.Torous.The Stochastic Volatility of Short-Term Interest Rates:Some International Evidence[J].The Journal of Finance,1999,54(6):2339-2359.
[10]谢赤,邓艺颖.基于扩散模型的银行间债券市场回购利率动态的实证分析[J].系统工程,2003,21(4):90-94.
[11]傅曼丽,董荣杰,屠梅曾.动态利率模型估计方法的一个实证检验[J].华中科技大学学报:自然科学版,2005,33(4):97-100.
[12]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[J].经济学,2006,5(2):511-532.
[13]林海,郑振龙.利率期限结构研究述评[J].管理科学学报,2007,10(1):79-93.
[14]高驰,郭艳红,于英琦.中国市场短期利率动态研究-基于有效矩方法的实证分析[J].南方经济,2007,4:45-55.
[15]Clark,P.K..A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices[J].Econometrica,1973,41(1):135-156.
[16]Tauchen,G.,M.Pitts.The Price Variability-Volume Relationship on Speculative Markets[J].Econometrica,1983,51(2):485-505.
[17]Gallant,A.R.,D.Hsieh,G.Tauchen.On Fitting a Recalcitrant Series:The Pound/Dollar Exchange Rate,1974-1983[J].Nonparametric and Semiparametric Methods in Econometrics and Statistics:Proceedings of the Fifth Intemational Symposium in Economic Theory and Econometrics,Cambridge University Press,1991.
[18]朱慧明,李峰,杨锦明.基于MCMC模拟的贝叶斯厚尾金融随机波动模型分析[J].运筹与管理,2007,16(4):111-115.
[19]周彦,张世英,张彤.跳跃连续时间SV模型建模及实证研究[J].系统管理学报,2007,16(5):531-536.
[20]李传乐,王美今.SV模型的模拟GMM方法——兼论涨跌停板制度的有效性[J].中山大学学报(自然科学版),2006,45(6):11-15.
[21]余素红,张世英.SV与GARCH模型对金融时间序列刻画能力的比较研究[J].系统工程,2002,20(5):28-33.
[22]孟利锋.随机波动模型及其建模方法研究[D].天津:天津大学,2004.
[23]Harvey,A.C.,E.Ruiz,N.Shephard.Multivariate Stochastic Variance Models[J].Review of Economic Studies,1994,61(2):247-264.
[24]Melino,A.,S.M.Tumbull.Pricing Foreign Currency Options with Stochastic Volatility[J].Journal of Econometrics,1990,45(1):239-265.
[25]Sorensen,M..Prediction Based Estimating Equations[J].Econometrics,2000,3:123-147.
[26]Gallant,A.R.,D.Hsie,G.Tauchen.Estimation of Stochastic Volatility Models with Diagnostics[J].Journal of Econometrics,1997,81(1):159-192.
[27]Sandmann,G.,S.J.Koopman.Estimation of Stochastic Volatility Models via Monte Carlo Maximum Likelihood[J].Journal of Econometrics,1998,87(2):271-301.
[28]Danielsson,J..Stochastic Volatility in Asset Prices:Estimation with Simulated Maximum Likelihood[J].Journal of Econometric s,1994,64(1):375-400.
[29]Jacquier,E.,Nicholas G.Poison,Peter E.Rossi.Bayesian Analysis of Stochastic Volatility Models[J].Journal of Business & Economic Statistics,1994,12(4):371-389.
[30]Shephard,N.,M.K.Pitt.Likelihood Analysis of Non-Gaussian Measurement Time Series[J].Biometrika,1997,84(3):653-667.
[31]Kim,S.,N.Shephard,S.Chib.Stochastic Volatility:Likelihood Inference and Comparison with ARCH Models[J].Review of Economic Studies,1998,65(3):361-393.
[32]Meyer,R.,Jun Yu.BUGS for a Bayesian Analysis of Stochastic Volatility Models[J].The Econometrics Journal,2000,3(2):198-215.
[33]张世英,樊智.协整理论与波动模型[M].北京:清华大学出版社,2004.
[34]Spiegelhalter,et al..Bayesian Measures of Model Complexity and Fit[J].Journal of the Royal Statistical Society,Series B(Statistical Methodology),2002,64(4):583-639.
[35]高占军.SHIBOR负重前行[EB/OL].http://www.caijing.com.cn/investor/zqsc/2007-01-24/15966.shtml,2007-1-24.