基于非参数贝叶斯方法的随机波动建模与应用
|
摘要
本文利用非参数贝叶斯方法进行随机波动建模。通常的参数随机波动模型适用于证券市场中的综合指数数据,而对个股数据和小范围指数数据的拟合效果较差,主要原因是其收益率数据的变化规律更为复杂、具有更厚的尾部行为,而非参数贝叶斯方法的随机波动模型无需进行分布假设,具有很强的灵活性。本文利用SV-DPM模型对IBM的股票价格数据和上证50指数数据进行建模,研究发现非参数随机波动模型能拟合参数随机波动模型难以扑捉到的数据特征,实证表明有充分的依据支持非参数贝叶斯随机波动模型。论文的研究有助于捕捉金融资产的时变波动性质,能更好的揭示金融市场的运行规律,为期权定价和金融风险管理提供依据,对于防范与控制金融风险有着重要意义。
In this paper, we use Bayesian nonparametric stochastic volatility modeling methods. Parametric stochastic volatility model is applicable to the stock market composite index data, individual stock price data and small-scale index data fitting result is not very good. Instead of parametric Bayesian model without distributional assumptions, it can learn directly from the probability distribution of the data,it is very flexible. We used the SV-DPM model to fit IBM's stock price data and the SSE 50 index.We found that non-parametric stochastic volatility model can found the data characteristics that the common parameter model is difficult to capture. Empirical evidence shows that there is a sufficient basis to support Bayesian nonparametric stochastic volatility model. The study enriched the discrete time stochastic volatility modeling method, and it is also helpful to capture the time-varying volatility of financial assets and reveal the rules of financial markets for assets within the framework of option price,provide decision-making basis for control financial risks and has important theoretical and practical significance for the financial system.
In this paper, we use Bayesian nonparametric stochastic volatility modeling methods. Parametric stochastic volatility model is applicable to the stock market composite index data, individual stock price data and small-scale index data fitting result is not very good. Instead of parametric Bayesian model without distributional assumptions, it can learn directly from the probability distribution of the data,it is very flexible. We used the SV-DPM model to fit IBM's stock price data and the SSE 50 index.We found that non-parametric stochastic volatility model can found the data characteristics that the common parameter model is difficult to capture. Empirical evidence shows that there is a sufficient basis to support Bayesian nonparametric stochastic volatility model. The study enriched the discrete time stochastic volatility modeling method, and it is also helpful to capture the time-varying volatility of financial assets and reveal the rules of financial markets for assets within the framework of option price,provide decision-making basis for control financial risks and has important theoretical and practical significance for the financial system.
引文
[1] Hull J, White A. The pricing of options on assets with stochastic volatilities[J]. Journal of Finance,1987, 42:281-300.
[2] Heston S L. A closed-form solution for options with stochastic volatility with applications to bond and currency options[J]. Review of financial studies, 1996, 6(2):327-343.
[3] Taylor S J. Modeling Financial Time Series Chichester[M]. John Wiley, 1986.
[4] Jacquier E, Polson N G, Rossi P E. Bayesian analysis of stochastic volatility models[J]. Journal of Business and Economic Statistics, 1994, 12:371-389.
[5] Kim S, Shephard N, Chib S. Stochastic volatility:Likelihood inference and comparison with ARCH models[J]. Review of Economic Studies, 1998, 65:361-393.
[6] Harvey A C, Shephard N. The estimation of an asymmetric stochastic volatility model for asset returns[J]. Journal of Business and Economic Statistics, 1996, 14:429-434.
[7] Omori Y, Chib S, Shephard N, Nakajima J. Stochastic volatility with leverage:Fast likelihood inference[J]. Journal of Econometrics, 2007, 140:425-449.
[8] Yu J. On leverage in a stochastic volatility model[J]. Journal of Econometrics, 2005, 127(2):165-178.
[9] Yu J. A semiparametric stochastic volatility model[J]. Journal of Econometrics, 2012, 167:473-482.
[10]郑振龙,刘晓曙.马尔可夫状态转换加随机波动瞬时利率模型实证研究[J].数理统计与管理,2009, 28(6):1067-1073.
[11]刘金全,李楠,郑挺国.随机波动模型的马尔可夫链-蒙特卡洛模拟方法一在沪市收益率序列上的应用[J].数理统计与管理,2010, 29(6):1026-1035.
[12]吴鑫育,马超群,汪寿阳.随机波动率模型的参数估计及对中国股市的实证[J].系统工程理论与实践,2014, 34(1):35-44.
[13]方国斌,张波.金融资产配置中的因子面板随机波动模型[J].统计研究,2014, 31(3):90-98.
[14] Gallant A R, Hsieh D, Tauchen G. Estimation of stochastic volatility models with diagnostics[J].Journal of Econometrics, 1997, 81(1):159-192.
[15] Mahieu R J, Schotman P C. An empirical application of stochastic volatility models[J]. Journal of Applied Econometrics, 1998, 13(4):333-360.
[16] Durham G B. Monte Carlo methods for estimating, smoothing, and filtering one and two-factor stochastic volatility models[J]. Journal of Econometrics, 2006,133(1):273-305.
[17] Chib S, Nardari F, Shephard N. Markov chain Monte Carlo methods for stochastic volatility models[J]. Journal of Econometrics, 2002, 108(2):281-316.
[18] Nakajima J, Omori Y. Leverage, heavy-tails and correlated jumps in stochastic volatility models[J].Computational Statistics&Data Analysis, 2009, 53:2335-2353.
[19]郑挺国.基于有限混合状态空间的金融随机波动模型及应用研究[D].吉林大学博士论,2009.
[20]蒋远营.随机波动模型的贝叶斯估计及其在金融市场中的应用[J].现代管理科学,2018,(7):48-50+120.
[21] Durham G B. SV mixture models with application to S&P 500 index return[J]. Journal of Financial Economics, 2007, 85:822-856.
[22] Jensen M J, Maheu J M. Semiparametric Bayesian inference of long-memory stochastic volatility models[J]. Journal of Time Series Analysis, 2004, 25(6):895-922.
[23] Jensen M J, Maheu J M. Bayesian semiparametric stochastic volatility modeling[J]. Journal of Econometrics, 2010, 157, 2:306-316.
[24] Griffin J E, Steel M F J. Ordered-based dependent Dirichlet processes[J]. Journal of the American Statistical Association, 2006, 101:179-194.
[25] Griffin J E, Steel M F J. Stick-breaking autoregressive processes[J]. Journal of Econometrics, 2011,162:383-396.
[26] Delatola E I, Griffin J E. Bayesian nonparametric modeling of the return distribution with stochastic volatility[J]. Bayesian Analysis, 2011, 6:1-26.
[27] Delatola E I, Griffin J E. A Bayesian semiparametric model for volatility with a leverage effect[J].Computational Statistics&Data Analysis, 2013, 60:97-110.
[28] Griffin J E. Default priors for density estimation with mixture models[J]. Bayesian Analysis, 2010,5:45-64.
[29] Jensen M J, Maheu J M. Estimating a semiparametric asymmetric stochastic volatility model with Dirichlet process mixture[J]. Journal of Econometrics, 2014, 178(3):523-538.
[30]蔡伟宏.基于非参数贝叶斯方法的资产配置[D].华中科技大学博士论文,2012.
[31]杨爱军,蒋学军,林金官,刘晓星.基于MCMC方法的金融贝叶斯半参数随机波动模型研究[J].数理统计与管理,2016, 35(5):817-825.
[32] Lo A Y. On a class of Bayesian nonparametric estimates:I. Density Estimates[J]. The Annals of Statistics, 1984, 12(1):351-357.
[33] Ferguson T S. Bayesian density estimation by mixtures of normal distributions[A]. In:Rizvi M H,Rustagi J, Siegmund D(eds.). Recent Advances In Statistics:Papers in Honor of Herman Cherno on His Sixtieth Birthday[C]. New York:Academic Press, 1983:287-302.
[34] Fuller W A. Introduction to Time Series(2nd ed.)[M]. New York:John Wiley, 1996.
[35]张波,蒋远营.基于中国股票高频交易数据的随机波动建模与应用[J].统计研究,2017, 34(3):107-117.
[2] Heston S L. A closed-form solution for options with stochastic volatility with applications to bond and currency options[J]. Review of financial studies, 1996, 6(2):327-343.
[3] Taylor S J. Modeling Financial Time Series Chichester[M]. John Wiley, 1986.
[4] Jacquier E, Polson N G, Rossi P E. Bayesian analysis of stochastic volatility models[J]. Journal of Business and Economic Statistics, 1994, 12:371-389.
[5] Kim S, Shephard N, Chib S. Stochastic volatility:Likelihood inference and comparison with ARCH models[J]. Review of Economic Studies, 1998, 65:361-393.
[6] Harvey A C, Shephard N. The estimation of an asymmetric stochastic volatility model for asset returns[J]. Journal of Business and Economic Statistics, 1996, 14:429-434.
[7] Omori Y, Chib S, Shephard N, Nakajima J. Stochastic volatility with leverage:Fast likelihood inference[J]. Journal of Econometrics, 2007, 140:425-449.
[8] Yu J. On leverage in a stochastic volatility model[J]. Journal of Econometrics, 2005, 127(2):165-178.
[9] Yu J. A semiparametric stochastic volatility model[J]. Journal of Econometrics, 2012, 167:473-482.
[10]郑振龙,刘晓曙.马尔可夫状态转换加随机波动瞬时利率模型实证研究[J].数理统计与管理,2009, 28(6):1067-1073.
[11]刘金全,李楠,郑挺国.随机波动模型的马尔可夫链-蒙特卡洛模拟方法一在沪市收益率序列上的应用[J].数理统计与管理,2010, 29(6):1026-1035.
[12]吴鑫育,马超群,汪寿阳.随机波动率模型的参数估计及对中国股市的实证[J].系统工程理论与实践,2014, 34(1):35-44.
[13]方国斌,张波.金融资产配置中的因子面板随机波动模型[J].统计研究,2014, 31(3):90-98.
[14] Gallant A R, Hsieh D, Tauchen G. Estimation of stochastic volatility models with diagnostics[J].Journal of Econometrics, 1997, 81(1):159-192.
[15] Mahieu R J, Schotman P C. An empirical application of stochastic volatility models[J]. Journal of Applied Econometrics, 1998, 13(4):333-360.
[16] Durham G B. Monte Carlo methods for estimating, smoothing, and filtering one and two-factor stochastic volatility models[J]. Journal of Econometrics, 2006,133(1):273-305.
[17] Chib S, Nardari F, Shephard N. Markov chain Monte Carlo methods for stochastic volatility models[J]. Journal of Econometrics, 2002, 108(2):281-316.
[18] Nakajima J, Omori Y. Leverage, heavy-tails and correlated jumps in stochastic volatility models[J].Computational Statistics&Data Analysis, 2009, 53:2335-2353.
[19]郑挺国.基于有限混合状态空间的金融随机波动模型及应用研究[D].吉林大学博士论,2009.
[20]蒋远营.随机波动模型的贝叶斯估计及其在金融市场中的应用[J].现代管理科学,2018,(7):48-50+120.
[21] Durham G B. SV mixture models with application to S&P 500 index return[J]. Journal of Financial Economics, 2007, 85:822-856.
[22] Jensen M J, Maheu J M. Semiparametric Bayesian inference of long-memory stochastic volatility models[J]. Journal of Time Series Analysis, 2004, 25(6):895-922.
[23] Jensen M J, Maheu J M. Bayesian semiparametric stochastic volatility modeling[J]. Journal of Econometrics, 2010, 157, 2:306-316.
[24] Griffin J E, Steel M F J. Ordered-based dependent Dirichlet processes[J]. Journal of the American Statistical Association, 2006, 101:179-194.
[25] Griffin J E, Steel M F J. Stick-breaking autoregressive processes[J]. Journal of Econometrics, 2011,162:383-396.
[26] Delatola E I, Griffin J E. Bayesian nonparametric modeling of the return distribution with stochastic volatility[J]. Bayesian Analysis, 2011, 6:1-26.
[27] Delatola E I, Griffin J E. A Bayesian semiparametric model for volatility with a leverage effect[J].Computational Statistics&Data Analysis, 2013, 60:97-110.
[28] Griffin J E. Default priors for density estimation with mixture models[J]. Bayesian Analysis, 2010,5:45-64.
[29] Jensen M J, Maheu J M. Estimating a semiparametric asymmetric stochastic volatility model with Dirichlet process mixture[J]. Journal of Econometrics, 2014, 178(3):523-538.
[30]蔡伟宏.基于非参数贝叶斯方法的资产配置[D].华中科技大学博士论文,2012.
[31]杨爱军,蒋学军,林金官,刘晓星.基于MCMC方法的金融贝叶斯半参数随机波动模型研究[J].数理统计与管理,2016, 35(5):817-825.
[32] Lo A Y. On a class of Bayesian nonparametric estimates:I. Density Estimates[J]. The Annals of Statistics, 1984, 12(1):351-357.
[33] Ferguson T S. Bayesian density estimation by mixtures of normal distributions[A]. In:Rizvi M H,Rustagi J, Siegmund D(eds.). Recent Advances In Statistics:Papers in Honor of Herman Cherno on His Sixtieth Birthday[C]. New York:Academic Press, 1983:287-302.
[34] Fuller W A. Introduction to Time Series(2nd ed.)[M]. New York:John Wiley, 1996.
[35]张波,蒋远营.基于中国股票高频交易数据的随机波动建模与应用[J].统计研究,2017, 34(3):107-117.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |