A New Approach to Volatility Modeling: The Factorial Hidden Markov Volatility Model

A new process—the factorial hidden Markov volatility (FHMV) model—is proposed to model financial returns or realized variances. Its dynamics are driven by a latent volatility process specified as a product of three components: a Markov chain controlling volatility persistence, an independent discrete process capable of generating jumps in the volatility, and a predictable (data-driven) process capturing the leverage effect. An economic interpretation is attached to each one of these components. Moreover, the Markov chain and jump components allow volatility to switch abruptly between thousands of states, and the transition matrix of the model is structured to generate a high degree of volatility persistence. An empirical study on six financial time series shows that the FHMV process compares favorably to state-of-the-art volatility models in terms of in-sample fit and out-of-sample forecasting performance over time horizons ranging from 1 to 100 days. Supplementary materials for this article are available online.     

市场流动性的状态转换及其突变点检测研究

通过构建AR-MS-GARCH模型,分析了市场流动性的状态转换机制,并设计了一种新的突变点检测指标。实证结果表明,市场流动性存在明显的"低—高"波动状态交替转换特征,两种状态都有较强的波动持续性,但不同状态转换和持续期存在一定的非对称性;计算突变点检测指标发现,市场流动性在样本期内存在五个突变点,而它们所对应的时刻往往是市场流动性"强—弱"转换的临界点。这些结论有助于监管部门及时采取政策措施,减少市场流动性突然逆转的可能性,以维护金融系统稳定。     

Testing for intercept‐scale switch in linear autoregression

Autoregressive models with switching regime are a frequently used class of nonlinear time series models, which are popular in finance, engineering, and other fields. We consider linear switching autoregressions in which the intercept and variance possibly switch simultaneously, while the autoregressive parameters are structural and hence the same in all states, and we propose quasi‐likelihood‐based tests for a regime switch in this class of models. Our motivation is from financial time series, where one expects states with high volatility and low mean together with states with low volatility and higher mean. We investigate the performance of our tests in a simulation study, and give an application to a series of IBM monthly stock returns. The Canadian Journal of Statistics 40: 427–446; 2012 © 2012 Statistical Society of Canada     

The Gibbs sampler with particle efficient importance sampling for state-space models*

We consider Particle Gibbs (PG) for Bayesian analysis of non-linear non-Gaussian state-space models. As a Monte Carlo (MC) approximation of the Gibbs procedure, PG uses sequential MC (SMC) importance sampling inside the Gibbs to update the latent states. We propose to combine PG with the Particle Efficient Importance Sampling (PEIS). By using SMC sampling densities which are approximately globally fully adapted to the targeted density of the states, PEIS can substantially improve the simulation efficiency of the PG relative to existing PG implementations. The efficiency gains are illustrated in PG applications to a non-linear local-level model and stochastic volatility models.     

A flexible particle Markov chain Monte Carlo method

Particle Markov Chain Monte Carlo methods are used to carry out inference in nonlinear and non-Gaussian state space models, where the posterior density of the states is approximated using particles. Current approaches usually perform Bayesian inference using either a particle marginal Metropolis–Hastings (PMMH) algorithm or a particle Gibbs (PG) sampler. This paper shows how the two ways of generating variables mentioned above can be combined in a flexible manner to give sampling schemes that converge to a desired target distribution. The advantage of our approach is that the sampling scheme can be tailored to obtain good results for different applications. For example, when some parameters and the states are highly correlated, such parameters can be generated using PMMH, while all other parameters are generated using PG because it is easier to obtain good proposals for the parameters within the PG framework. We derive some convergence properties of our sampling scheme and also investigate its performance empirically by applying it to univariate and multivariate stochastic volatility models and comparing it to other PMCMC methods proposed in the literature.     

基于Twin-SVM的多分形金融市场风险的智能预警研究

本文以沪深300指数（CSI300）长达11年时间的5分钟高频交易数据为研究样本,首先提出一种基于多分形特征的金融市场正常与关注状态的界定方法,并引入新型的支持向量机（SVM）人工智能模型,即孪生SVM（Twin-SVM）模型对多分形特征下的金融市场风险展开预警研究。实证结果表明：（1）中国新兴金融市场的价格波动具有显著的多分形特征;（2）基于多分形特征参数界定的正常与关注状态不仅准确,而且也具有明显的统计检验意义和明确的现实意义;（3）与传统SVM和BP神经网络（NN）相比,Twin-SVM在预测精度上不仅显著更高,而且在预测稳定性上也明显更优,即Twin-SVM能够有效地解决其它预警模型存在的非对称样本问题。     

Quantile forecasts for financial volatilities based on parametric and asymmetric models

For financial volatilities such as realized volatility and volatility index, a new parametric quantile forecast strategy is proposed, focusing on forecast interval and value at risk (VaR) forecast. This fully addresses asymmetries in 3 parts: mean, volatility and distribution. The asymmetries are addressed by the LHAR (leverage heterogeneous autoregressive) model of McAleer and Medeiros (2008) and Corsi and Reno (2009) for the mean part, by the EGARCH model for the volatility part, and by the skew-t distribution for the error distribution part. The method is applied to the realized volatilities and the volatility indexes of the US S&P 500 index, the US NASDAQ index, the Korea KOSPI index in which significant asymmetries are identified. Considerable out-of-sample forecast improvements of the forecast interval and VaR forecast are demonstrated for the volatilities: forecast intervals of volatilities have better coverages with shorter lengths and VaR forecasts of volatility indexes have better violations if asymmetries are properly addressed rather than ignored. The proposed parametric method reveals considerably better out-of-sample performance than the recently proposed semiparametric quantile regression approach of Zikes and Barunik (2016).     

Sampling-based Inference of Time Deformation Models with Heavy Tail Distributions

This article focuses on simulation-based inference for the time-deformation models directed by a duration process. In order to better capture the heavy tail property of the time series of financial asset returns, the innovation of the observation equation is subsequently assumed to have a Student-t distribution. Suitable Markov chain Monte Carlo (MCMC) algorithms, which are hybrids of Gibbs and slice samplers, are proposed for estimation of the parameters of these models. In the algorithms, the parameters of the models can be sampled either directly from known distributions or through an efficient slice sampler. The states are simulated one at a time by using a Metropolis-Hastings method, where the proposal distributions are sampled through a slice sampler. Simulation studies conducted in this article suggest that our extended models and accompanying MCMC algorithms work well in terms of parameter estimation and volatility forecast.     

Volatility,Momentum, and Time-Varying Skewness in Foreign Exchange Returns

This article tests a stochastic volatility model of exchange rates that links both the level of volatility and its instantaneous covariance with returns to pathwise properties of the currency. In particular, the model implies that the return–volatility covariance behaves like a weighted average of recent returns and hence switches signs according to the direction of trends in the data. This implies that the skewness of the finite-horizon return distribution likewise switches sign, leading to time-varying implied volatility “smiles” in options prices. The model is fit and assessed using Bayesian techniques. Some previously reported volatility results are accounted for by the fitted models. The predicted pattern of skewness dynamics accords well with that found in historical options prices.     

Continuous Time Wishart Process for Stochastic Risk

Risks are usually represented and measured by volatility–covolatility matrices. Wishart processes are models for a dynamic analysis of multivariate risk and describe the evolution of stochastic volatility–covolatility matrices, constrained to be symmetric positive definite. The autoregressive Wishart process (WAR) is the multivariate extension of the Cox, Ingersoll, Ross (CIR) process introduced for scalar stochastic volatility. As a CIR process it allows for closed-form solutions for a number of financial problems, such as term structure of T-bonds and corporate bonds, derivative pricing in a multivariate stochastic volatility model, and the structural model for credit risk. Moreover, the Wishart dynamics are very flexible and are serious competitors for less structural multivariate ARCH models.     

Bayesian Analysis of Stochastic Volatility Models

New techniques for the analysis of stochastic volatility models in which the logarithm of conditional variance follows an autoregressive model are developed. A cyclic Metropolis algorithm is used to construct a Markov-chain simulation tool. Simulations from this Markov chain converge in distribution to draws from the posterior distribution enabling exact finite-sample inference. The exact solution to the filtering/smoothing problem of inferring about the unobserved variance states is a by-product of our Markov-chain method. In addition, multistep-ahead predictive densities can be constructed that reflect both inherent model variability and parameter uncertainty. We illustrate our method by analyzing both daily and weekly data on stock returns and exchange rates. Sampling experiments are conducted to compare the performance of Bayes estimators to method of moments and quasi-maximum likelihood estimators proposed in the literature. In both parameter estimation and filtering, the Bayes estimators outperform these other approaches.     

Modeling the Dependence of Conditional Correlations on Market Volatility

Several models have been developed to capture the dynamics of the conditional correlations between time series of financial returns and several studies have shown that the market volatility is a major determinant of the correlations. We extend some models to include explicitly the dependence of the correlations on the market volatility. The models differ by the way—linear or nonlinear, direct or indirect—in which the volatility influences the correlations. Using a wide set of models with two measures of market volatility on two datasets, we find that for some models, the empirical results support to some extent the statistical significance and the economic significance of the volatility effect on the correlations, but the presence of the volatility effect does not improve the forecasting performance of the extended models. Supplementary materials for this article are available online.     

预期引导、政策冲击与股市波动——基于文本分析法的异质性诊断

防范股票市场异常波动是维护金融稳定和防控金融风险的关键一环。货币政策实践中,预期引导与政策冲击对股市波动的实际影响和传导机制迥然不同。现有文献对两者之于股票市场波动 的异质性影响多有讨论,但分歧明显。基于2005年到2019年中国人民银行各季度《货币政策执行报告》和《货币政策大事记》,本文分别构建表征货币政策预期引导强度和实际操作频度的代理变量,对上述指标之于同期A股市场主要行业指数的波动性影响做了多维诊断和系统梳理。研究发现,第一,预期引导效应和政策冲击效应对于股票市场波动性的影响存在显著异质性特征,预期引导有助于平抑市场波动,而频繁调控则会放大股市波动。第二,预期引导的明确性会制约其对股市波动的平缓作用,货币调控意愿的表达越明确,越有助于平抑股票市场波动;而更坚决的“严厉型”表述比态度相对温和的“温和型”表述能够更显著地平抑股票市场波动。第三,实际操作频度对股市波动的放大作用受制于具体调控方向,宽松型调控的频率上升仅会小幅放大股市波动,而紧缩型货币调控则会大幅抬升股市波动性。由此,从平抑股市异常波动、维持金融稳定的角度出发,强化货币政策的预期引导比相机抉择的频繁调控更为重要;在预期引导过程中,应当增强调控意愿表达的明确性和坚决性,以限制其对金融市场运行带来的扰动。     

Forecasting interest rates volatilities by GARCH (1,1) and stochastic volatility models

In this paper, we compare the forecast ability of GARCH(1,1) and stochastic volatility models for interest rates. The stochastic volatility is estimated using Markov chain Monte Carlo methods. The comparison is based on daily data from 1994 to 1996 for the ten year swap rates for Deutsch Mark, Japanese Yen, and Pound Sterling. Various forecast horizons are considered. It turns out that forecasts based on stochastic volatility models are in most cases superiour to those obtained by GARCH(1,1) models.     

The Relationship between the Volatility of Returns and the Number of Jumps in Financial Markets

We propose a methodology to employ high frequency financial data to obtain estimates of volatility of log-prices which are not affected by microstructure noise and Lévy jumps. We introduce the “number of jumps” as a variable to explain and predict volatility and show that the number of jumps in SPY prices is an important variable to explain the daily volatility of the SPY log-returns, has more explanatory power than other variables (e.g., high and low, open and close), and has a similar explanatory power to that of the VIX. Finally, the number of jumps is very useful to forecast volatility and contains information that is not impounded in the VIX.     

基于函数型自适应聚类的股票收益波动模式比较

股票收益波动具有典型的连续函数特征,将其纳入连续动态函数范畴分析,能够挖掘现有离散分析方法不能揭示的深层次信息。本文基于连续动态函数视角研究上证50指数样本股票收益波动的类别模式和时段特征。首先由实际离散观测数据信息自行驱动,重构隐含在其中的本征收益波动函数。进一步,利用函数型主成分正交分解收益函数波动的主趋势,在无核心信息损失的主成分降维基础上,引入自适应权重聚类分析客观划分股票收益函数波动的模式类别。最后,利用函数型方差分析检验不同类别收益函数之间波动差异的显著性和稳健性,并基于波动函数周期性时段划分,图形展示和可视化剖析每一类别收益函数在不同时段波动的势能转化规律。研究发现：上证综指股票收益波动的主导趋势可以分解为四个子模式,50只股票存在五类显著的波动模式类别,并且5类波动模式的特征差异主要体现在本次研究区间的初始阶段。本文拓展了股票收益波动模式分类和差异因素分析的研究视角,能够为金融监管部门的管理策略制定和证券市场的投资组合配置提供实证支持。     

Fourier-cosine method for pricing forward starting options with stochastic volatility and jumps

This article provides an efficient method for pricing forward starting options under stochastic volatility model with double exponential jumps. The forward characteristic function of the log asset price is derived and thereby forward starting options are well evaluated by Fourier-cosine technique. Based on adaptive simulated annealing algorithm, the model is calibrated to obtain the estimated parameters. Numerical results show that the pricing method is accurate and fast. Double exponential jumps have pronounced impacts on long-term forward starting options prices. Stochastic volatility model with double exponential jumps fits forward implied volatility smile pretty well in contrast to stochastic volatility model.     

基于高维波动率网络模型的股票市场风险特征研究

波动率是金融风险管理研究的重要内容之一。本文基于复杂网络理论和数据挖掘技术提出股票市场的高维波动率网络模型。首先运用互信息度量不同股票价格波动之间的相关关系,其次对股票市场不同周期下的波动情况建立度的中心势、平均距离、幂律分布等网络拓扑指标,再次根据这些指标利用Prim算法构建出高维波动率网络模型,最后运用Newman-Girvan算法对股票价格波动率的相关性进行分层研究。高维波动率网络模型突破了传统波动率模型关于变量维数的限制,能够在依赖少量假设的基础上,挖掘出多个金融市场主体间的相互关系,反映金融市场的风险特征及网络拓扑性质。实证结果发现：与常用的Pearson相关系数法相比,在互信息框架下,股价波动的非线性相关关系得到了更好的度量;股票市场的整体波动性与个股波动率相关性变化趋势相反,市场处在高波动时期资产组合分散化效果较好;网络中存在少量度数大的关键节点和中心节点,风险通过这些节点可以迅速传递到整个市场;股票市场的运行具有明显的行业聚集现象;网络分层研究进一步直观的展现了风险在层与层之间的传递规律和与之对应的行业特征。高维波动率网络模型为挖掘股票市场的风险特征与管理金融风险提供了一个新的工具。     

Forecast Evaluation in the Presence of Unobserved Volatility

A number of volatility forecasting studies have led to the perception that the ARCH- and Stochastic Volatility-type models provide poor out-of-sample forecasts of volatility. This is primarily based on the use of traditional forecast evaluation criteria concerning the accuracy and the unbiasedness of forecasts. In this paper we provide an analytical assessment of volatility forecasting performance. We use the volatility and log volatility framework to prove how the inherent noise in the approximation of the true- and unobservable-volatility by the squared return, results in a misleading forecast evaluation, inflating the observed mean squared forecast error and invalidating the Diebold-Mariano statistic. We analytically characterize this noise and explicitly quantify its effects assuming normal errors. We extend our results using more general error structures such as the Compound Normal and the Gram-Charlier classes of distributions. We argue that evaluation problems are likely to be exacerbated by non-normality of the shocks and that non-linear and utility-based criteria can be more suitable for the evaluation of volatility forecasts.     

Foreign Exchange Intervention by the Bank of Japan: Bayesian Analysis Using a Bivariate Stochastic Volatility Model

A bivariate stochastic volatility model is employed to measure the effect of intervention by the Bank of Japan (BOJ) on daily returns and volume in the USD/YEN foreign exchange market. Missing observations are accounted for, and a data-based Wishart prior for the precision matrix of the errors to the transition equation that is in line with the likelihood is suggested. Empirical results suggest there is strong conditional heteroskedasticity in the mean-corrected volume measure, as well as contemporaneous correlation in the errors to both the observation and transition equations. A threshold model is used for the BOJ reaction function, which is estimated jointly with the bivariate stochastic volatility model via Markov chain Monte Carlo. This accounts for endogeneity between volatility in the market and the BOJ reaction function, something that has hindered much previous empirical analysis in the literature on central bank intervention. The empirical results suggest there was a shift in behavior by the BOJ, with a movement away from a policy of market stabilization and toward a role of support for domestic monetary policy objectives. Throughout, we observe “leaning against the wind” behavior, something that is a feature of most previous empirical analysis of central bank intervention. A comparison with a bivariate EGARCH model suggests that the bivariate stochastic volatility model produces estimates that better capture spikes in in-sample volatility. This is important in improving estimates of a central bank reaction function because it is at these periods of high daily volatility that central banks more frequently intervene.