基于Markov状态转换下多元随机波动率模型的动态套期保值研究
|
摘要
在全球经济一体化过程中,国内企业的生产经营活动日益受到国际市场上原材料与商品价格的影响,尤其在08年国际金融危机爆发之后,国内企业面临着巨大的商品价格波动风险,国内企业纷纷寻找办法分散价格风险,从近几年的国内企业调查看来,原材料和产品的市场价格直接决定了企业的生存情况,所以规避价格风险是国内企业赖以生存前提。衍生品市场的发展为解决这一问题提供了有效方案,期货市场的一个重要功能是通过期货套期保值锁定商品价格,规避价格风险。本文研究的核心是利用期货合约的套期保值功能分散价格波动风险,文章旨在通过对比不同的套期保值模型,寻找最优套期保值率,提高期货套期保值的效果。
目前研究套期保值策略主要是利用GARCH模型,但该模型存在了很大的问题,GARCH模型在刻画随机性上存在严重的不足。本文利用多元随机波动率模型(MSV模型)对套期保值进行研究,多元随机波动率模型是一类异方差模型,它将随机过程引入模型之中,能够比GARCH模型更好的反应金融市场波动的随机性,是刻画金融市场波动性的最理想的模型。
本文首先利用固定相关系数多元随机波动率模型(CC-MSV)建立基于CC-MSV的风险最小套期保值模型来研究最优套期保值率。然后在CC-MSV模型的基础上上引入动态相关模型和t分布,建立基于厚尾的动态相关系数多元随机波动率模型(DC-t-MSV)的方差最小套期保值模型,该模型考虑了金融数据的尖峰厚尾的特点以及现货与期货的对数收益率的相关系数之间的局部相关性,更加符合金融时间序列的特点。最后,由于金融市场具有一定的脆弱性,容易受到类似于经济危机、自然灾害、经济政策变化等外部突发事件的影响,所以本文基于DC-t-MSV模型,引入了马尔科夫转换机制(regime-switching)来表示突发状况对期货市场的影响,建立了基于马尔科夫状态转换下厚尾的动态相关系数多元随机波动率模型(RSDC-t-MSV)的方差最小套期保值模型,RSDC-t-MSV模型及考虑了金融数据的内部特征又考虑了外部突发事件对金融市场的影响,符合金融市场的实际情况。
文章的实证部分以2008年1月10日到2011年6月30日的黄金期货与现货价格的对数收益率数据为研究对象,利用该数据分别对CC-MSV模型、DC-t-MSV模型、RSDC-t-MSV模型在套期保值领域的应用加以研究,利用套期保值测度公式对比这三种模型的套期保值效果。实证研究中首先利用Eviews5.0对数据的统计特征加以分析,然后利用winbugs软件对模型进行编程运算。文章的参数估计部分采用MCMC方法中的切片抽样技术,该技术与Gibbs抽样相比能够有效的所点参数估计所需要的时间。
通过对黄金期货套期保值效率的实证分析得到了理想的结论。三种模型所得到的最优套期保值率都是动态的,都取得了满意的套期保值效果,但是经过对比分析表明:利用RSDC-t-MSV模型计算最优套期保值率既能捕捉到市场的剧烈波动,又能保证套期保值率的稳定性,与DC-t-MSV模型和CC-MSV模型相比具有很大的优势。从套期保值效果看,RSDC-t-MSV模型能更大程度的降低黄金期货与现货的资产组合投资的风险,它的套期保值效果优于DC-t-MSV模型和CC-MSV模型。因此,可以认为利用RSDC-t-MSV模型进行套期保值能够更好的规避价格风险。文章实证分析的结论与理论分析完全吻合。
In the process of global economic integration, the domestic enterprise's production and operating activities increasingly influenced by the price of international market raw material and commodity, especially in the 08 years after the outbreak of the financial crisis in domestic enterprises are facing tremendous commodity price risk. Especially after the outbreak of the international financial crisis in 2008, domestic enterprises are facing a huge risk of commodity price fluctuations. The companies are looking for ways to disperse the price risk. The market price of raw materials and products determine the enterprise's survival directly, so to avoid price risk is the prerequisite for the survival and development of domestic enterprises. The derivatives markets provide an effective solution to this program; an important function of futures market is locking the commodity prices and avoiding price risk through the futures hedge. The core of this study is using the function of hedge of futures contracts to spread the risk of price volatility. The article aims to compare among the different hedging models, find out the optimal hedge ratio and increase the effect of futures hedging.
Current research of hedging strategy is based on GARCH model, but this model has a big problem, this model has serious shortcomings in characterize randomness. In this paper, we adopt multivariate stochastic volatility model (MSV model) to study hedge, multiple stochastic volatility model is a class of heteroscedastic models, and it introduced stochastic process into the model. Compared with GARCH, it will be better to reflect than the randomness of financial markets. It is the optimal models to depict financial market volatility.
In this paper, firstly, we build minimum variance hedge model with CC-MSV model to study the optimal hedge ratio. Then based on CC-MSV model, we introduce dynamic correlation model and multivariate t-distribution. This new model is named DC-t-MSV. The model has considered the peak and fat-tail characteristics of financial data as well as the local correlation of the correlation coefficient between the spot and futures’logarithmic returns, which is more in line with the characteristics of financial time series. Finally, because of the vulnerability of financial market, the develop of financial market will suffered from unexpected events ,such as economic crises, natural disasters, changes in external economic policy and so on. So based on DC-t-MSV model, the article introduce Markov regime switching (regime -switching) to build the RSDC-t-MSV minimum variance hedge model to represent the sudden impact on the futures market. RSDC-t-MSV model has considered both the internal features of the financial data and external contingencies. It is consistent with the actual situation of financial markets.
In the empirical part, the article uses logarithmic return of gold’s spot and future price from January 10, 2008 to June 30, 2011 to do empirical research. The data are used for CC-MSV model, DC-t-MSV model and RSDC-t-MSV model to study on hedging; it also uses hedging measure formula to compare the hedging effect based on the three different models. During the empirical research, we begin with the use of Eviews5.0 to analyze the statistical characteristics of data, and then use winbugs to compute the model. In the part of Parameter estimation, the article applies slice sampling techniques of MCMC methods. This technology can be more effective compared with the Gibbs sampling.
The empirical analysis of gold futures hedging efficiency has come to the desirable conclusion. Three models have obtained the dynamic optimal hedge ratio. All of them have achieved a satisfactory effect of hedging. However, comparative analysis shows that the optimal hedge ratio calculated by the RSDC-t-MSV model not only can capture the market volatility, but also ensure the stability of the hedge rate. It has great advantage compared with DC-t-MSV model and CC-MSV model. From the side of hedge effort, RSDC-t-MSV model can achieve a greater degree of reduction of the portfolio investment risk. It can do well in hedge than CC-MSV model and DC-t-MSV model. Therefore, we can consider that the use of RSDC-t-MSV model can do better in the area of hedge. The empirical analysis is fully consistent with the theoretical analysis.
目前研究套期保值策略主要是利用GARCH模型,但该模型存在了很大的问题,GARCH模型在刻画随机性上存在严重的不足。本文利用多元随机波动率模型(MSV模型)对套期保值进行研究,多元随机波动率模型是一类异方差模型,它将随机过程引入模型之中,能够比GARCH模型更好的反应金融市场波动的随机性,是刻画金融市场波动性的最理想的模型。
本文首先利用固定相关系数多元随机波动率模型(CC-MSV)建立基于CC-MSV的风险最小套期保值模型来研究最优套期保值率。然后在CC-MSV模型的基础上上引入动态相关模型和t分布,建立基于厚尾的动态相关系数多元随机波动率模型(DC-t-MSV)的方差最小套期保值模型,该模型考虑了金融数据的尖峰厚尾的特点以及现货与期货的对数收益率的相关系数之间的局部相关性,更加符合金融时间序列的特点。最后,由于金融市场具有一定的脆弱性,容易受到类似于经济危机、自然灾害、经济政策变化等外部突发事件的影响,所以本文基于DC-t-MSV模型,引入了马尔科夫转换机制(regime-switching)来表示突发状况对期货市场的影响,建立了基于马尔科夫状态转换下厚尾的动态相关系数多元随机波动率模型(RSDC-t-MSV)的方差最小套期保值模型,RSDC-t-MSV模型及考虑了金融数据的内部特征又考虑了外部突发事件对金融市场的影响,符合金融市场的实际情况。
文章的实证部分以2008年1月10日到2011年6月30日的黄金期货与现货价格的对数收益率数据为研究对象,利用该数据分别对CC-MSV模型、DC-t-MSV模型、RSDC-t-MSV模型在套期保值领域的应用加以研究,利用套期保值测度公式对比这三种模型的套期保值效果。实证研究中首先利用Eviews5.0对数据的统计特征加以分析,然后利用winbugs软件对模型进行编程运算。文章的参数估计部分采用MCMC方法中的切片抽样技术,该技术与Gibbs抽样相比能够有效的所点参数估计所需要的时间。
通过对黄金期货套期保值效率的实证分析得到了理想的结论。三种模型所得到的最优套期保值率都是动态的,都取得了满意的套期保值效果,但是经过对比分析表明:利用RSDC-t-MSV模型计算最优套期保值率既能捕捉到市场的剧烈波动,又能保证套期保值率的稳定性,与DC-t-MSV模型和CC-MSV模型相比具有很大的优势。从套期保值效果看,RSDC-t-MSV模型能更大程度的降低黄金期货与现货的资产组合投资的风险,它的套期保值效果优于DC-t-MSV模型和CC-MSV模型。因此,可以认为利用RSDC-t-MSV模型进行套期保值能够更好的规避价格风险。文章实证分析的结论与理论分析完全吻合。
In the process of global economic integration, the domestic enterprise's production and operating activities increasingly influenced by the price of international market raw material and commodity, especially in the 08 years after the outbreak of the financial crisis in domestic enterprises are facing tremendous commodity price risk. Especially after the outbreak of the international financial crisis in 2008, domestic enterprises are facing a huge risk of commodity price fluctuations. The companies are looking for ways to disperse the price risk. The market price of raw materials and products determine the enterprise's survival directly, so to avoid price risk is the prerequisite for the survival and development of domestic enterprises. The derivatives markets provide an effective solution to this program; an important function of futures market is locking the commodity prices and avoiding price risk through the futures hedge. The core of this study is using the function of hedge of futures contracts to spread the risk of price volatility. The article aims to compare among the different hedging models, find out the optimal hedge ratio and increase the effect of futures hedging.
Current research of hedging strategy is based on GARCH model, but this model has a big problem, this model has serious shortcomings in characterize randomness. In this paper, we adopt multivariate stochastic volatility model (MSV model) to study hedge, multiple stochastic volatility model is a class of heteroscedastic models, and it introduced stochastic process into the model. Compared with GARCH, it will be better to reflect than the randomness of financial markets. It is the optimal models to depict financial market volatility.
In this paper, firstly, we build minimum variance hedge model with CC-MSV model to study the optimal hedge ratio. Then based on CC-MSV model, we introduce dynamic correlation model and multivariate t-distribution. This new model is named DC-t-MSV. The model has considered the peak and fat-tail characteristics of financial data as well as the local correlation of the correlation coefficient between the spot and futures’logarithmic returns, which is more in line with the characteristics of financial time series. Finally, because of the vulnerability of financial market, the develop of financial market will suffered from unexpected events ,such as economic crises, natural disasters, changes in external economic policy and so on. So based on DC-t-MSV model, the article introduce Markov regime switching (regime -switching) to build the RSDC-t-MSV minimum variance hedge model to represent the sudden impact on the futures market. RSDC-t-MSV model has considered both the internal features of the financial data and external contingencies. It is consistent with the actual situation of financial markets.
In the empirical part, the article uses logarithmic return of gold’s spot and future price from January 10, 2008 to June 30, 2011 to do empirical research. The data are used for CC-MSV model, DC-t-MSV model and RSDC-t-MSV model to study on hedging; it also uses hedging measure formula to compare the hedging effect based on the three different models. During the empirical research, we begin with the use of Eviews5.0 to analyze the statistical characteristics of data, and then use winbugs to compute the model. In the part of Parameter estimation, the article applies slice sampling techniques of MCMC methods. This technology can be more effective compared with the Gibbs sampling.
The empirical analysis of gold futures hedging efficiency has come to the desirable conclusion. Three models have obtained the dynamic optimal hedge ratio. All of them have achieved a satisfactory effect of hedging. However, comparative analysis shows that the optimal hedge ratio calculated by the RSDC-t-MSV model not only can capture the market volatility, but also ensure the stability of the hedge rate. It has great advantage compared with DC-t-MSV model and CC-MSV model. From the side of hedge effort, RSDC-t-MSV model can achieve a greater degree of reduction of the portfolio investment risk. It can do well in hedge than CC-MSV model and DC-t-MSV model. Therefore, we can consider that the use of RSDC-t-MSV model can do better in the area of hedge. The empirical analysis is fully consistent with the theoretical analysis.
引文
[1]王宜峰,王春发,蒋一琛基于DC-t-MSV模型的套期保值研究[J],西部论坛,2011,第21卷,第五期:104-108
[2]安文莹多元t分布的尾部性质及其在股票市场的应用[J],贵州工业大学学报(社会科学版),2008,第10卷,第1期:43-44+47
[3]蔡风景,李元.基于体制转换模型的动态相关系数研究[J].统计与信息论坛,2010,25(1):14-18.
[4]方晓炜.中国信贷周期研究—基于马尔可夫体制转换模型的分析[D].厦门:厦门大学,2008.
[5]付剑茹,张宗成,龚金林基于MCMC模拟的期货最优套期保比贝叶斯分析[J],管理工程学报,2009,第23卷,第3期:120-125+134
[6]蒋祥林,王春峰,吴晓霖.基于状态转移ARCH模型的中国股市波动性研究[J].系统工程学报,2004,19(3):270-277.
[7]李阿庭.我国短期利率的马尔可夫体制转换模型的实证分析[D].厦门:厦门大学,2008.
[8]刘凤芹,吴喜之随机波动模型参数估计的新算法及其在上海股市的实证[J],系统工程理论与实践,2006,第4期:27-31
[9]徐永坤基于随机波动模型的中国股市波动性实证研究[D]复旦大学2008
[10]张光远关于多元t分布的一些讨论[J]新疆大学学报1996.3 33-38
[11]张红喜基于多元随机波动率模型的动态套期保值研究[D]大连理工大学2008
[12]张嘉为,郑桂环.基于状态转移模型的条件期望与方差一从2状态到N状态的推广[J].系统科学与数学,2008,28(11):398—1406.
[13]张瑞锋,张世英基于VS-MSV模型的金融市场波动溢出分析及实证研究[J]系统工程2007.8 1-6
[14]张振中.受控的带马氏调制跳扩散过程及其在保险金融中的应用[D].长沙:中南大学,2009.
[15]周颖,张红喜,迟国泰基于DC-MSV的动态套期保值模型及实证研究[J],系统管理学报,2008,第17卷,第4期:409-417
[16]Andrea Buraschi, Paolo Porchia, Fabio Trohani Correlation Risk and Optimal Portfolio Choice [J],The Journal of Finance,2010,392-420
[17]Ang A and G. Bekaert . Regime Switches in Interest Rates ,forthcoming[J].Journal of Business and Economic Statistics,2001.
[18]Anne Gron, Bj?rn N. J?rgensen, Nicholas G. Polson Optimal Portfolio Choice and Stochastic Volatility [J] , Applied Stochastic models in Business and Industry 2011,237-256
[19]Aparna V. Huzurbazar Bayesian Prediction for Flowgraph Models. Flowgraph Models for Multistate Time-to-Event Data[J], 2004: 89–128
[20]Avraham Kamara Issues in futures markets: A survey Journal of Futures Markets[J], 1982, Volume 2, Issue 3: 261–294.
[21]Bansal R and H Zhou.Term Structure of Interest Rates with Regime Shifts[J].Journal of Finance,2003.
[22]Billio M,Pelizzon L.Value-at-Risk:A multivariate switching regime approach.Journal of Empirical Finance[J].2000,vol.7:531—554.
[23]Bollerslve, T. Generalized Autoregressive Conditional Heteroscedasticity[J]. Journal of Econometrics.1986,31:307-327
[24]Boudoukh,Jacob et al.Regime Shifts and Bond Returns.Working paper,New York University,1999.
[25]Buffington J,Elliott R. J.American options with regime switching[J].Int. J. Theor. Appl. Finance,2002,vol. 5:497-514.
[26]Carmen Broto & Esther Ruiz. Estimation methods for stochastic volatility models: a survey[J] . Journal of Economic Surveys, 2004, Volume 18, Issue 5: 613–649.
[27]Carolyn W. Chang and Jack S. K. Chang Optimum futures hedge in the presence of clustered supply and demand shocks, stochastic basis, and firm's costs of hedging[J]. Journal of Futures Markets. 2003,Volume 23, Issue 12: 1209–1237,
[28]Chih-Chiang Hsu, Chih-Ping Tseng and Yaw-Huei Wang Dynamic hedging with futures: A copula-based GARCH model Journal of Futures Markets[J], November 2008, Volume 28, Issue 11: 1095–1116.
[29]Chris Brooks & Apostolos Katsaris A Three-Regime Model of Speculative Behaviour: Modelling the Evolution of the S&P 500 Composite Index[J]. The Economic Journal. 2005,Volume 115, Issue 505: 767–797,
[30]Christophe Andrieu, Arnaud Doucet and Roman Holenstein Particle Markov chain Monte Carlo methods. Journal of the Royal Statistical Society: Series B[J] (Statistical Methodology),2010, Volume 72, Issue 3: 269–342.
[31]Cindy L. Yu, Haitao Li and Martin T. Wells MCMC estimation of LéVY jumpmodels using stock and option prices[J], Mathematical Finance, 2011,Volume 21, Issue 3: 383–422,
[32]C.-D. Fuh,R.-H. Wang.Option pricing in a Black-Scholes model with Markov switching[J].Working Paper,Institute of Statistical Science,2002.
[33]Christian P. Robert, Jean-Michel Marin, Judith Rousseau Bayesian Inference and Computation[J]. Handbook of Statistical Systems Biology, 2011, 39–65,
[34]D D Yao, Q Zhang,X Y Zhou.A regime-switching model for European options, Stochastic Processes.Optimization and Control Theory Applications in Financial Engineering[J],Queueing Networks and Manufacturing Systems,2006:281–300.
[35]Donald Lien and Y. K. Tse Some Recent Developments in Futures Hedging[J]. Journal of Economic Surveys, 2002, Volume 16, Issue 3: 357–396.
[36]Elliott R J,Osakwe C -J U.Option pricing for pure jump processes with Markov switching compensators[J].Finance and Stochastics,2006,vol. 10:250-275.
[37]Engle. R. F, Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation[J]. Econometrica. 1982, 50:987-1007
[38]Eric Terry Minimum-variance futures hedging under alternative return specifications[J], Journal of Futures Markets. 2005,Volume 25, Issue 6: 537–552,
[39]Fbng W M and See K H.A Markov switching model of the conditional volatility of crude oil futuresprices[J].Energy Economics,2002,vol.24:71-95.
[40]Fred Espen Benth, The stochastic volatility model of barndorff-nielsen and shephard in commodity markets[J]. Mathematical Finance. 2011, Volume 21, Issue 4: 595–625.
[41]F L Yuen ,H Yang.Pricing Asian Options and Equity-Indexed Annuities with Regime switching by the trinomial tree method[J].North American Actuarial Journal,2010,vol.7:256-277.
[42]Garcia R and P Perron.An Analysis of the Real Interest Rate Under regime Shifts[J].Review of Economics and Statistics,1996,vol.78:111-125.
[43]Gray S.Modeling the Conditional Distribution of Interest Rates as a Regime-Switching Process[J].Journal of Financial Economics,1996,vol.42:27-62.
[44]Hamilton J.Rational Expectations Econometric Analysis of Changes in Regimes: An Investigation of the Term Structure of Interest Rates[J].Journal of Economic Dynamics and Control,1998,vol.12:385-423.
[45]Hazem Daouk and Jie Qun Guo Switching asymmetric GARCH and options on a volatility index[J]. Journal of Futures Markets. 2004, Volume 24, Issue 3: 251–282.
[46]Hsiang-Tai Lee A copula-based regime-switching GARCH model for optimal futures hedging. Journal of Futures Markets, 2009 Volume 29, Issue 10: 946–972.
[47]J.Buffington,R. J. Elliott.American options with regime switching[J], International Journal of Theoretical and Applied Finance,2002,vol.5:497–514.
[48]Jerry Coakley, Jian Dollery & Neil Kellard Long memory and structural breaks in commodity futures markets[J]. Journal of Futures Markets. 2011,Volume 31, Issue 11: 1076–1113.
[49]Johan Kilander.Calibrating an option pricing model under regime-switching volatility[J].2007.
[50]José-María Montero, Gema Fernández-Avilés & María-Carmen García Estimation of Asymmetric Stochastic Volatility Models: Application to Daily Average Prices of Energy Products[J], International Statistical Review, 2010, Volume 78, Issue 3,: 330–347,
[51]Jun Yu multivariate stochastic volatility model: Bayesian estimation and model comparison [J]. Econometric Review, 2006, 361-384
[52]Liu R H, Zhang Q,Yin G.Option Pricing in a Regume-Switching Model Using the Fast Fourier Ttransform[J].Journal of Applied Mathematics and Stochastic Analysis,Volume 2006:1-22.
[53]Luc Bauwens, Arie Preminger and Jeroen V. K. Rombouts Theory and inference for a Markov switching GARCH model[J]. The Econometrics Journal. 2010, Volume 13, Issue 2: 218–244
[54]Manabu Asai, Michael McAleer, Jun Yu Multivariate Stochastic Volatility: A Review [J], Econometric Reviews, 2006, 145-175
[55]Mike K. P. So, C. Y. Choi A threshold factor multivariate stochastic volatility model [J],Journal of Forecasting,2009,712-73
[56]M Pemy,Q Zhang.Optimal stock liquidation in a regime switching model with finite time horizon[J].Journal of Mathematical Analysis and Applications,2006: 537–552.
[57]Naik V and M H Lee.Yield Curve Dynamics with Discrete Shifts in Economic Regimes:Theory and Estimation[J].Working paper, University of British Columbia,1997.
[58]ederington,L.H. The Hedging Performance of the New Future Market[J]. Journalof Finance, 1979, 34:157-170
[59]Malliaris. A. G. &Urrutia. J.L. The impact of the lengths of estimation periods and hedging horizons on the effectiveness of a hedge: Evidence from foreign currency future[J]. Journal of Futures Markets. 1991, 3: 271-289.
[60]Manabu Asai & Michael McAleer Multivariate stochastic volatility, leverage and news impact surfaces[J]. The Econometrics Journal. 2009, Volume 12, Issue 2: 292–309
[61]Mike K. P. So & C. Y. Choi A threshold factor multivariate stochastic volatility model[J]. Journal of Forecasting.2009, Volume 28, Issue 8: 712–735
[62]Richard D. F. Harris, Jian Shen and Evarist Stoja The Limits to Minimum-Variance Hedging[J], Journal of Business Finance & Accounting, 2010, Volume 37, Issue 5-6: 737–761.
[63]Ruey S. Tsay, Multivariate Volatility Models and Their Applications. Analysis of Financial Time Series Third Edition[M] 2010 : 505–555
[64]Simon Jackman Implementing Markov Chain Monte Carlo[J]. Bayesian Analysis for the Social Sciences, 2009: 251–297
[65]Wai Mun Fong and Kim Hock See Modelling the conditional volatility of commodity index futures as a regime switching process[J]. Journal of Applied Econometrics, 2001Volume 16, Issue 2: 133–163.
[2]安文莹多元t分布的尾部性质及其在股票市场的应用[J],贵州工业大学学报(社会科学版),2008,第10卷,第1期:43-44+47
[3]蔡风景,李元.基于体制转换模型的动态相关系数研究[J].统计与信息论坛,2010,25(1):14-18.
[4]方晓炜.中国信贷周期研究—基于马尔可夫体制转换模型的分析[D].厦门:厦门大学,2008.
[5]付剑茹,张宗成,龚金林基于MCMC模拟的期货最优套期保比贝叶斯分析[J],管理工程学报,2009,第23卷,第3期:120-125+134
[6]蒋祥林,王春峰,吴晓霖.基于状态转移ARCH模型的中国股市波动性研究[J].系统工程学报,2004,19(3):270-277.
[7]李阿庭.我国短期利率的马尔可夫体制转换模型的实证分析[D].厦门:厦门大学,2008.
[8]刘凤芹,吴喜之随机波动模型参数估计的新算法及其在上海股市的实证[J],系统工程理论与实践,2006,第4期:27-31
[9]徐永坤基于随机波动模型的中国股市波动性实证研究[D]复旦大学2008
[10]张光远关于多元t分布的一些讨论[J]新疆大学学报1996.3 33-38
[11]张红喜基于多元随机波动率模型的动态套期保值研究[D]大连理工大学2008
[12]张嘉为,郑桂环.基于状态转移模型的条件期望与方差一从2状态到N状态的推广[J].系统科学与数学,2008,28(11):398—1406.
[13]张瑞锋,张世英基于VS-MSV模型的金融市场波动溢出分析及实证研究[J]系统工程2007.8 1-6
[14]张振中.受控的带马氏调制跳扩散过程及其在保险金融中的应用[D].长沙:中南大学,2009.
[15]周颖,张红喜,迟国泰基于DC-MSV的动态套期保值模型及实证研究[J],系统管理学报,2008,第17卷,第4期:409-417
[16]Andrea Buraschi, Paolo Porchia, Fabio Trohani Correlation Risk and Optimal Portfolio Choice [J],The Journal of Finance,2010,392-420
[17]Ang A and G. Bekaert . Regime Switches in Interest Rates ,forthcoming[J].Journal of Business and Economic Statistics,2001.
[18]Anne Gron, Bj?rn N. J?rgensen, Nicholas G. Polson Optimal Portfolio Choice and Stochastic Volatility [J] , Applied Stochastic models in Business and Industry 2011,237-256
[19]Aparna V. Huzurbazar Bayesian Prediction for Flowgraph Models. Flowgraph Models for Multistate Time-to-Event Data[J], 2004: 89–128
[20]Avraham Kamara Issues in futures markets: A survey Journal of Futures Markets[J], 1982, Volume 2, Issue 3: 261–294.
[21]Bansal R and H Zhou.Term Structure of Interest Rates with Regime Shifts[J].Journal of Finance,2003.
[22]Billio M,Pelizzon L.Value-at-Risk:A multivariate switching regime approach.Journal of Empirical Finance[J].2000,vol.7:531—554.
[23]Bollerslve, T. Generalized Autoregressive Conditional Heteroscedasticity[J]. Journal of Econometrics.1986,31:307-327
[24]Boudoukh,Jacob et al.Regime Shifts and Bond Returns.Working paper,New York University,1999.
[25]Buffington J,Elliott R. J.American options with regime switching[J].Int. J. Theor. Appl. Finance,2002,vol. 5:497-514.
[26]Carmen Broto & Esther Ruiz. Estimation methods for stochastic volatility models: a survey[J] . Journal of Economic Surveys, 2004, Volume 18, Issue 5: 613–649.
[27]Carolyn W. Chang and Jack S. K. Chang Optimum futures hedge in the presence of clustered supply and demand shocks, stochastic basis, and firm's costs of hedging[J]. Journal of Futures Markets. 2003,Volume 23, Issue 12: 1209–1237,
[28]Chih-Chiang Hsu, Chih-Ping Tseng and Yaw-Huei Wang Dynamic hedging with futures: A copula-based GARCH model Journal of Futures Markets[J], November 2008, Volume 28, Issue 11: 1095–1116.
[29]Chris Brooks & Apostolos Katsaris A Three-Regime Model of Speculative Behaviour: Modelling the Evolution of the S&P 500 Composite Index[J]. The Economic Journal. 2005,Volume 115, Issue 505: 767–797,
[30]Christophe Andrieu, Arnaud Doucet and Roman Holenstein Particle Markov chain Monte Carlo methods. Journal of the Royal Statistical Society: Series B[J] (Statistical Methodology),2010, Volume 72, Issue 3: 269–342.
[31]Cindy L. Yu, Haitao Li and Martin T. Wells MCMC estimation of LéVY jumpmodels using stock and option prices[J], Mathematical Finance, 2011,Volume 21, Issue 3: 383–422,
[32]C.-D. Fuh,R.-H. Wang.Option pricing in a Black-Scholes model with Markov switching[J].Working Paper,Institute of Statistical Science,2002.
[33]Christian P. Robert, Jean-Michel Marin, Judith Rousseau Bayesian Inference and Computation[J]. Handbook of Statistical Systems Biology, 2011, 39–65,
[34]D D Yao, Q Zhang,X Y Zhou.A regime-switching model for European options, Stochastic Processes.Optimization and Control Theory Applications in Financial Engineering[J],Queueing Networks and Manufacturing Systems,2006:281–300.
[35]Donald Lien and Y. K. Tse Some Recent Developments in Futures Hedging[J]. Journal of Economic Surveys, 2002, Volume 16, Issue 3: 357–396.
[36]Elliott R J,Osakwe C -J U.Option pricing for pure jump processes with Markov switching compensators[J].Finance and Stochastics,2006,vol. 10:250-275.
[37]Engle. R. F, Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation[J]. Econometrica. 1982, 50:987-1007
[38]Eric Terry Minimum-variance futures hedging under alternative return specifications[J], Journal of Futures Markets. 2005,Volume 25, Issue 6: 537–552,
[39]Fbng W M and See K H.A Markov switching model of the conditional volatility of crude oil futuresprices[J].Energy Economics,2002,vol.24:71-95.
[40]Fred Espen Benth, The stochastic volatility model of barndorff-nielsen and shephard in commodity markets[J]. Mathematical Finance. 2011, Volume 21, Issue 4: 595–625.
[41]F L Yuen ,H Yang.Pricing Asian Options and Equity-Indexed Annuities with Regime switching by the trinomial tree method[J].North American Actuarial Journal,2010,vol.7:256-277.
[42]Garcia R and P Perron.An Analysis of the Real Interest Rate Under regime Shifts[J].Review of Economics and Statistics,1996,vol.78:111-125.
[43]Gray S.Modeling the Conditional Distribution of Interest Rates as a Regime-Switching Process[J].Journal of Financial Economics,1996,vol.42:27-62.
[44]Hamilton J.Rational Expectations Econometric Analysis of Changes in Regimes: An Investigation of the Term Structure of Interest Rates[J].Journal of Economic Dynamics and Control,1998,vol.12:385-423.
[45]Hazem Daouk and Jie Qun Guo Switching asymmetric GARCH and options on a volatility index[J]. Journal of Futures Markets. 2004, Volume 24, Issue 3: 251–282.
[46]Hsiang-Tai Lee A copula-based regime-switching GARCH model for optimal futures hedging. Journal of Futures Markets, 2009 Volume 29, Issue 10: 946–972.
[47]J.Buffington,R. J. Elliott.American options with regime switching[J], International Journal of Theoretical and Applied Finance,2002,vol.5:497–514.
[48]Jerry Coakley, Jian Dollery & Neil Kellard Long memory and structural breaks in commodity futures markets[J]. Journal of Futures Markets. 2011,Volume 31, Issue 11: 1076–1113.
[49]Johan Kilander.Calibrating an option pricing model under regime-switching volatility[J].2007.
[50]José-María Montero, Gema Fernández-Avilés & María-Carmen García Estimation of Asymmetric Stochastic Volatility Models: Application to Daily Average Prices of Energy Products[J], International Statistical Review, 2010, Volume 78, Issue 3,: 330–347,
[51]Jun Yu multivariate stochastic volatility model: Bayesian estimation and model comparison [J]. Econometric Review, 2006, 361-384
[52]Liu R H, Zhang Q,Yin G.Option Pricing in a Regume-Switching Model Using the Fast Fourier Ttransform[J].Journal of Applied Mathematics and Stochastic Analysis,Volume 2006:1-22.
[53]Luc Bauwens, Arie Preminger and Jeroen V. K. Rombouts Theory and inference for a Markov switching GARCH model[J]. The Econometrics Journal. 2010, Volume 13, Issue 2: 218–244
[54]Manabu Asai, Michael McAleer, Jun Yu Multivariate Stochastic Volatility: A Review [J], Econometric Reviews, 2006, 145-175
[55]Mike K. P. So, C. Y. Choi A threshold factor multivariate stochastic volatility model [J],Journal of Forecasting,2009,712-73
[56]M Pemy,Q Zhang.Optimal stock liquidation in a regime switching model with finite time horizon[J].Journal of Mathematical Analysis and Applications,2006: 537–552.
[57]Naik V and M H Lee.Yield Curve Dynamics with Discrete Shifts in Economic Regimes:Theory and Estimation[J].Working paper, University of British Columbia,1997.
[58]ederington,L.H. The Hedging Performance of the New Future Market[J]. Journalof Finance, 1979, 34:157-170
[59]Malliaris. A. G. &Urrutia. J.L. The impact of the lengths of estimation periods and hedging horizons on the effectiveness of a hedge: Evidence from foreign currency future[J]. Journal of Futures Markets. 1991, 3: 271-289.
[60]Manabu Asai & Michael McAleer Multivariate stochastic volatility, leverage and news impact surfaces[J]. The Econometrics Journal. 2009, Volume 12, Issue 2: 292–309
[61]Mike K. P. So & C. Y. Choi A threshold factor multivariate stochastic volatility model[J]. Journal of Forecasting.2009, Volume 28, Issue 8: 712–735
[62]Richard D. F. Harris, Jian Shen and Evarist Stoja The Limits to Minimum-Variance Hedging[J], Journal of Business Finance & Accounting, 2010, Volume 37, Issue 5-6: 737–761.
[63]Ruey S. Tsay, Multivariate Volatility Models and Their Applications. Analysis of Financial Time Series Third Edition[M] 2010 : 505–555
[64]Simon Jackman Implementing Markov Chain Monte Carlo[J]. Bayesian Analysis for the Social Sciences, 2009: 251–297
[65]Wai Mun Fong and Kim Hock See Modelling the conditional volatility of commodity index futures as a regime switching process[J]. Journal of Applied Econometrics, 2001Volume 16, Issue 2: 133–163.
© 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 |