【作者】 郑挺国；

【导师】 刘金全；

【作者基本信息】 吉林大学 ， 数量经济学， 2009， 博士

【摘要】 近年来,金融随机波动(SV)模型广泛地应用于金融经济学、数理金融学和计量经济学领域,专门用以捕捉金融市场金融资产时变波动性,并对金融决策制定产生重要的影响,是现代金融学理论界与实务界中一种非常重要的波动模型。目前SV模型在金融计量学界正方兴未艾,虽然取得了一系列的研究成果,但计算上较为简单、而算法相对有效的估计方法迄今研究不足。本文对已有研究文献进行了广泛的调研和系统的综述,重点讨论SV模型、扩展模型和马尔科夫转移SV模型的近似估计,并对我国沪深股票收益率和市场短期利率展开实证分析,论文主要工作和创新如下:一、讨论了高斯混合状态空间模型、马尔科夫转移状态空间模型以及马尔科夫转移高斯混合状态空间模型的确切分析,推导了这些模型的确切滤波、确切似然函数,依次提出了依赖于控制参数的三种近似滤波,以及相应的近似似然函数和近似平滑技术,并通过随机模拟实验讨论了近似估计方法的准确性。二、基于高斯混合近似滤波方法给出了SV模型、扩展SV模型和马尔科夫转移SV模型的近似估计方法;通过随机模拟实验,将近似估计方法与粒子滤波方法、传统估计方法进行了拟合准度分析,参数估计有限样本性质分析,从而评估了近似估计方法应用于SV模型的可行性。三、利用SV类模型分析了沪深股市收益率、短期拆借利率序列的时变波动性,证明了SV模型比GARCH类模型具有更好的预测能力,证明了近似方法与贝叶斯方法和蒙特卡罗似然具有可比性,证实了沪深股市波动性、短期利率波动性中均存在明显的区制转移特征,证实了忽略波动结构性突变可能导致波动持续性高估的事实,并且发现利率波动不仅存在均值转移,还存在波动持续性和波动的波动转移,而且这种波动转移性与我国经济增长率变化有一定的联系。更多还原

【Abstract】 In recent years, stochastic volatility (SV) class of models are widely used in areas offinancial economics and mathematical finance. They can capture time-varying volatilities offinancial assets, and have important impacts on financial decision-making. The developmentof SV models is highly interdisciplinary, covering relevant theories and contents of financialeconomics, probability and statistics theory, and econometrics. They provide us with help tounderstand methods and models of real option pricing, e?ective asset allocation and accuraterisk assessment. As e?ective methods for describing time-varying volatility of an financialassets, the studies on the SV models have important theoretical significance and practicalsignificance.The SV class of models is a basic alternative to autoregressive conditional heteroscedastic(GARCH) class of models, but they provide a more ?exible structure for describing the time-varying volatility. As the model adds an error term in the dynamics of volatility introducinganother source of randomness, it has been found to fit asset returns better, have residualscloser to standard normal and have better statistical properties. However, they are typicalnonlinear non-Gaussian state space models, with the exact likelihood function being a highlycomplex and high-dimensional integration in analytical, leading to parameters and latent log-volatilities very di?cult to estimate. Although several extended SV models can be furtherused to examine some practical problems, such as asymmetric e?ect or leverage e?ect betweenvolatilities and returns, volatility clustering, volatility persistence and structural break, theyare more complex and thus too di?cult to estimate. Thus, searching for a computationallysimple and algorithmically e?ective estimation method is still the subject to explore in financialeconometrics, but also a major concern in this article.This paper carries out a series of studies around SV models. Facing some problems fromthe basic SV model and their extension, we review and sum up past researches, carding thetheoretical relation between SV models and modern finance. We mainly discuss estimationmethods for the basic SV model, extended SV models and the Markov-switching SV model.Then these models are applied to return data of China’s Shanghai and Shenzhen stock market,and short-term lending interest rate of bank credit market.In many parameter estimation methods for the basic SV model, some studies advocateto use the Markov chain Monte Carlo procedure or the simulated expected maximum pro- cedure, through taking the square and the logarithm of the SV model, and approximatingthe log-chi-square distribution by a mixture of normal distributions. However, the maximumlikelihood estimation procedure for this transformed SV model has not yet been put forward.Not only that, but approximate estimation of the coupled model for Gaussian mixture process,Markov switching process and state space process has also not been presented in time serieseconometrics. Based on the exact analysis of Gaussian mixture state space model, Markovswitching state space model, and Markov switching Gaussian mixture state space model, wedevelop three approximate filters, i.e. AMF(k), MSAMF(k), and MSMIXAMF(k) respectively,and the corresponding approximate maximum likelihood estimators and smoothing techniques.With these approximate filter, approximate maximum likelihood estimator and approximatesmoothing, this paper presents estimation methods for the basic SV model, the extended SVmodel, and the Markov switching SV model. The approximate estimation results are alsocompared to the results from the particle filter.The proposed approximate methods are examined by many simulation analysis usingsimulated data and repeated trials. The results show that our methods for Gaussian mixturestate space model, Markov switching state space model, and their coupled model work quitewell. The approximate filters have high accuracy, with the fitted results to the true stateprocess closing to the exact filters. Even with a smaller value of parameter k, they are also veryaccurate. Moreover, simulation results from the Gaussian mixture state space model also showthat parameter estimates are almost same under di?erent k using the approximate maximumlikelihood estimator. Similarly, simulation experiments for the basic SV model show that theapproximate filter (AMF) is very close to the particle filter, better than the Monte Carlolikelihood (MCL) filter (Koopman & Uspensky, 2002) when the number of simulation is smalland the Kalman filter. For the sample performance of parameter estimates, our approximatemaximum likelihood (AML) estimator performs competitively with the MCL estimtor when thenumber of simulation is large and the N-ML estimtor suggested by Fridman & Harris (1998),better than the QMl estimator based on the Kalman filter. At last, simulation experimentsfor the Markov switching SV model show that the approximate filter MSMIXAMF(k) notonly can better fit to the log-volatility process than MSAMF(k), but also can well describethe hidden Markov process under the true data generation process. Moreover, it is shownthat the approximate filter for the Markov switching Gaussian mixture state space model,MSMIXAMF(k), is obviously much better than that for the Markov-switching state spacemodel, MSAMF(k), while the latter will be the Kim approximate filter suggested by Kim(1994) when k = 1.Equipped with the SV models and the approximate methods introduced in this study, wecarried out empirical analysis on returns of China’s Shanghai and Shenzhen stock market andshort-term bank lending rate. On the one hand, we compare the in-sample performance of time-varying volatilities with di?erent models and di?erent estimation methods. Firstly, the fittedresults from GARCH-type models and SV-type models with return data and short-term interestrate data show that the SV models have higher explanatory power in modeling time-varying volatility, with stronger tail fitting e?ect. Secondly, we implement Bayesian Markov chainMonte Carlo estimation (JPR estimator and KSC estimator), QML estimator, MCL estimatorand proposed AML estimator for the basic SV model. It is shown that our AML estimatorperforms competitively with the Bayesian estimation methods and the MCL estimator. Theresults from the particle filter further show that the AML estimator is slightly better thanthe Bayesian estimation methods and the MCL estimator. Finally, with introducing leveragee?ects and regime switching, we compare in-sample performance of the basic SV model, theasymmetric SV model and the Markov switching SV model to stock returns and short terminterest rate.On the other hand, this study e?ectively tests and describes dynamic characteristics ofChina’s stock returns and short-term interest rate using di?erent SV models, so as to provideus with basic results for financial risk management and decision-making. First of all, althoughthe Shanghai stock returns and Shenzhen stock returns share a common trend at the majorityof periods, the di?erences between them can be described by the GARCH-type models and theSV-type models. For instance, Shanghai stock market has obvious leverage e?ect, while thereis no leverage e?ects in Shenzhen stock market. Both stock market volatilities of Shanghaiand Shenzhen have obvious regime-switching characteristics. In the majority of time periodsregime shifts are the same for them, but in 1995 and early 1996 Shanghai stock market takesa high-volatility regime, while Shenzhen stock market is in a low-volatility regime. Secondly,level e?ects are found between the time-varying volatility and the level of short-term interestrate, the estimated values of them are less than one using the SV-type models. Moreover,the results from the asymmetric SV model show the existence of leverage e?ect between theinterest rate volatility and interest rates, and the results from the Markov switching SV modelsshow obvious regime shifts in interest rate volatility. Finally, the results also show that interestrate volatilities not only have regime switching between high and low volatilities, but also haveobvious regime shifts between volatility consistence and volatility of volatility at the sametime. Thus our study reveals an internal mechanism that the short-term lending rate volatilitychange between a low volatility - low persistence - high volatility of volatility regime and a highvolatility - high persistence - low volatility of volatility regime. In addition, this study also findthat the regime switching characteristics have an obvious linkage with the GDP growth rate inChina’s macroeconomy, which further demonstrates the importance of interest rate volatility.更多还原