Bayesian analysis of stochastic volatility models with flexible tails

An alternative distributional assumption is proposed for the stochastic volatility model. This results in extremely flexible tail behaviour of the sampling distribution for the observables, as well as in the availability of a simple Markov Chain Monte Carlo strategy for posterior analysis. By allowing the tail behaviour to be determined by a separate parameter, we reserve the parameters of the volatility process to dictate the degree of volatility clustering. Treatment of a mean function is formally integrated in the analysis.

Some empirical examples on both stock prices and exchange rates clearly indicate the presence of fat tails, in combination with high levels of volatility clustering. In addition, predictive distributions indicate a good fit with these typical financial data sets.     

Integrated OU Processes and Non-Gaussian OU-based Stochastic Volatility Models

Abstract. In this paper, we study the detailed distributional properties of integrated non-Gaussian Ornstein–Uhlenbeck (intOU) processes. Both exact and approximate results are given. We emphasize the study of the tail behaviour of the intOU process. Our results have many potential applications in financial economics, as OU processes are used as models of instantaneous variance in stochastic volatility (SV) models. In this case, an intOU process can be regarded as a model of integrated variance. Hence, the tail behaviour of the intOU process will determine the tail behaviour of returns generated by SV models.     

Extremal memory of stochastic volatility with an application to tail shape inference

We characterize joint tails and tail dependence for a class of stochastic volatility processes. We derive the exact joint tail shape of multivariate stochastic volatility with innovations that have a regularly varying distribution tail. This is used to give four new characterizations of tail dependence. In three cases tail dependence is a non-trivial function of linear volatility memory parametrically represented by tail scales, while tail power indices do not provide any relevant dependence information. Although tail dependence is associated with linear volatility memory, tail dependence itself is nonlinear. In the fourth case a linear function of tail events and exceedances is linearly independent. Tail dependence falls in a class that implies the celebrated Hill (1975) tail index estimator is asymptotically normal, while linear independence of nonlinear tail arrays ensures the asymptotic variance is the same as the iid case. We illustrate the latter finding by simulation.     

Volatility model selection for extremes of financial time series

Although both widely used in the financial industry, there is quite often very little justification why GARCH or stochastic volatility is preferred over the other in practice. Most of the relevant literature focuses on the comparison of the fit of various volatility models to a particular data set, which sometimes may be inconclusive due to the statistical similarities of both processes. With an ever growing interest among the financial industry in the risk of extreme price movements, it is natural to consider the selection between both models from an extreme value perspective. By studying the dependence structure of the extreme values of a given series, we are able to clearly distinguish GARCH and stochastic volatility models and to test statistically which one better captures the observed tail behaviour. We illustrate the performance of the method using some stock market returns and find that different volatility models may give a better fit to the upper or lower tails.     

面板数据加权聚类分析方法研究

在面板数据聚类分析方法的研究中,基于面板数据兼具截面维度和时间维度的特征,对欧氏距离函数进行了改进,在聚类过程中考虑指标权重与时间权重,提出了适用于面板数据聚类分析的"加权距离函数"以及相应的Ward.D聚类方法。首先定义了考虑指标绝对值、邻近时点增长率以及波动变异程度的欧氏距离函数;然后,将指标权重与时间权重通过线性模型集结成综合加权距离,最终实现面板数据的加权聚类过程。实证分析结果显示,考虑指标权重与时间权重的面板数据加权聚类分析方法具有更好的分辨能力,能提高样本聚类的准确性。     

股票日内交易数据特征和波幅的分析

一、引言随着计算技术的发展和存储成本的降低 ,人们已经可以获取和分析日内股票交易的数据 ,这些数据对于金融市场研究的重要领域———金融市场微结构理论和实证金融经济计量学的研究产生了重要推动作用。 90年代以来 ,在实证金融经济计量研究中出现了对高频金融数据建模和分析的领域 ,即以日内交易数据为基础 ,去揭示交易过程的机制和统计特征。高频金融交易数据分析模型从 90年代开始迅速发展 ,目前已广泛地用于金融市场微结构理论的应用和实证检验。在有关研究领域中 ,市场参与者的行为以及交易过程的统计规律和特征的描述是研究关注的…     

Empirical Performance and Asset Pricing in Hidden Markov Models

Abstract

To improve the empirical performance of the Black-Scholes model, many alternative models have been proposed to address leptokurtic feature, volatility smile, and volatility clustering effects of the asset return distributions. However, analytical tractability remains a problem for most alternative models. In this article, we study a class of hidden Markov models including Markov switching models and stochastic volatility models, that can incorporate leptokurtic feature, volatility clustering effects, as well as provide analytical solutions to option pricing. We show that these models can generate long memory phenomena when the transition probabilities depend on the time scale. We also provide an explicit analytic formula for the arbitrage-free price of the European options under these models. The issues of statistical estimation and errors in option pricing are also discussed in the Markov switching models.     

混合贝塔分布随机波动模型及其贝叶斯分析

为了更准确地揭示金融资产收益率数据的真实数据生成过程,提出了基于混合贝塔分布的随机波动模型,讨论了混合贝塔分布随机波动模型的贝叶斯估计方法,并给出了一种Gibbs抽样算法。以上证A股综指简单收益率为例,分别建立了基于正态分布和混合贝塔分布的随机波动模型,研究表明,基于混合贝塔分布的随机波动模型更准确地描述了样本数据的真实数据生成过程,而正态分布的随机波动模型将高峰厚尾等现象归结为波动冲击,从而低估了收益率的平均波动水平,高估了波动的持续性和波动的冲击扰动。     

The Volatility of Realized Volatility

In recent years, with the availability of high-frequency financial market data modeling realized volatility has become a new and innovative research direction. The construction of “observable” or realized volatility series from intra-day transaction data and the use of standard time-series techniques has lead to promising strategies for modeling and predicting (daily) volatility. In this article, we show that the residuals of commonly used time-series models for realized volatility and logarithmic realized variance exhibit non-Gaussianity and volatility clustering. We propose extensions to explicitly account for these properties and assess their relevance for modeling and forecasting realized volatility. In an empirical application for S&P 500 index futures we show that allowing for time-varying volatility of realized volatility and logarithmic realized variance substantially improves the fit as well as predictive performance. Furthermore, the distributional assumption for residuals plays a crucial role in density forecasting.     

The Volatility of Realized Volatility

In recent years, with the availability of high-frequency financial market data modeling realized volatility has become a new and innovative research direction. The construction of “observable” or realized volatility series from intra-day transaction data and the use of standard time-series techniques has lead to promising strategies for modeling and predicting (daily) volatility. In this article, we show that the residuals of commonly used time-series models for realized volatility and logarithmic realized variance exhibit non-Gaussianity and volatility clustering. We propose extensions to explicitly account for these properties and assess their relevance for modeling and forecasting realized volatility. In an empirical application for S&P 500 index futures we show that allowing for time-varying volatility of realized volatility and logarithmic realized variance substantially improves the fit as well as predictive performance. Furthermore, the distributional assumption for residuals plays a crucial role in density forecasting.     

Clustering of financial instruments using jump tail dependence coefficient

In this paper, we propose a new clustering procedure for financial instruments. Unlike the prevalent clustering procedures based on time series analysis, our procedure employs the jump tail dependence coefficient as the dissimilarity measure, assuming that the observed logarithm of the prices/indices of the financial instruments are embedded into multidimensional Lévy processes. The efficiency of our proposed clustering procedure is tested by a simulation study. Finally, with the help of the real data of country indices we illustrate that our clustering procedure could help investors avoid potential huge losses when constructing portfolios.     

Tail density estimation for exploratory data analysis using kernel methods

It is often critical to accurately model the upper tail behaviour of a random process. Nonparametric density estimation methods are commonly implemented as exploratory data analysis techniques for this purpose and can avoid model specification biases implied by using parametric estimators. In particular, kernel-based estimators place minimal assumptions on the data, and provide improved visualisation over scatterplots and histograms. However kernel density estimators can perform poorly when estimating tail behaviour above a threshold, and can over-emphasise bumps in the density for heavy tailed data. We develop a transformation kernel density estimator which is able to handle heavy tailed and bounded data, and is robust to threshold choice. We derive closed form expressions for its asymptotic bias and variance, which demonstrate its good performance in the tail region. Finite sample performance is illustrated in numerical studies, and in an expanded analysis of the performance of global climate models.     

中国大豆期货收益GARCH效应的实证研究

文章研究了中国大连商品交易所大豆期货连续合约1994-2003年收益时间序列,并以该序列2003年第一个样本数据为分界点,建立了两子序列,分别进行了统计学分析,发现两子序列分布均是非正态的,较正态分布有尖峰厚尾的特征,具有记忆效应。并且,进一步根据两子序列的波动集群性建立一系列GARCH模型,对中国大豆期货的两个收益序列的波动性进行分析,并比较了二者的异同。     

中国农产品价格波动特征的实证研究——基于广义误差分布的ARCH类模型

近年来农产品价格波动频繁,结构特征明显,主要是因为受到生猪、棉花、大豆、胶脂果实类林产品和稻谷等农作物价格波动的影响.利用广义误差分布的ARCH类模型对主要农产品价格波动特征进行分析,结果表明:棉花价格没有显著的异方差效应;生猪、大豆和稻谷的价格波动具有显著的集聚性,但其市场并没有表现出高风险高回报的特征;稻谷价格波动具有显著的非对称性,但大豆和生猪的价格波动没有显著的非对称性.基于GED的ARCH类模型提高了模型的拟合效果,可以更好地分析中国主要农产品价格波动特征.     

Long memory and data frequency in financial markets

This paper investigates persistence in financial time series at three different frequencies (daily, weekly and monthly). The analysis is carried out for various financial markets (stock markets, FOREX, commodity markets) over the period from 2000 to 2016 using two different long memory approaches (R/S analysis and fractional integration) for robustness purposes. The results indicate that persistence is higher at lower frequencies, for both returns and their volatility. This is true of the stock markets (both developed and emerging) and partially of the FOREX and commodity markets examined. Such evidence against the random walk behaviour implies predictability and is inconsistent with the Efficient Market Hypothesis (EMH), since abnormal profits can be made using trading strategies based on trend analysis.     

上证指数收益率的特征及其波动性分析

股票价格的频繁波动是股票市场最明显的特征之一。ARCH类模型可以很好地预测金融资产收益率的方差。通过对上证指数的统计分析表明,上证指数的收益率分布表现出非正态性,并存在自回归条件异方差的特征。利用ARCH类模型对上证指数的波动进行了拟合,结果表明GARCH(1,1)模型对上证指数波动具有较好的拟合效果。     

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。     

Extreme quantile estimation based on financial time series

Estimation of market risk is an important problem in finance. Two well-known risk measures, viz., value at risk and median shortfall, turn out to be extreme quantiles of the marginal distribution of asset return. Time series on asset returns are known to exhibit certain stylized facts, such as heavy tails, skewness, volatility clustering, etc. Therefore, estimation of extreme quantiles in the presence of such features in the data seems to be of natural interest. It is difficult to capture most of these stylized facts using one specific time series model. This motivates nonparametric and extreme value theory-based estimation of extreme quantiles that do not require exact specification of the asset return model. We review these quantile estimators and compare their known properties. Their finite sample performance are compared using Monte Carlo simulation. We propose a new estimator that exhibits encouraging finite sample performance while estimating extreme quantile in the right tail region.     

Particle Learning for Fat-Tailed Distributions

It is well known that parameter estimates and forecasts are sensitive to assumptions about the tail behavior of the error distribution. In this article, we develop an approach to sequential inference that also simultaneously estimates the tail of the accompanying error distribution. Our simulation-based approach models errors with a t_ν-distribution and, as new data arrives, we sequentially compute the marginal posterior distribution of the tail thickness. Our method naturally incorporates fat-tailed error distributions and can be extended to other data features such as stochastic volatility. We show that the sequential Bayes factor provides an optimal test of fat-tails versus normality. We provide an empirical and theoretical analysis of the rate of learning of tail thickness under a default Jeffreys prior. We illustrate our sequential methodology on the British pound/U.S. dollar daily exchange rate data and on data from the 2008–2009 credit crisis using daily S&P500 returns. Our method naturally extends to multivariate and dynamic panel data.     

ARFIMAX and ARFIMAX-TARCH realized volatility modeling

ARFIMAX models are applied in estimating the intra-day realized volatility of the CAC40 and DAX30 indices. Volatility clustering and asymmetry characterize the logarithmic realized volatility of both the indices. The ARFIMAX model with time-varying conditional heteroskedasticity is the best performing specification and, at least in the case of DAX30, provides statistically superior next trading day's realized volatility forecasts.