隐含高阶协矩:提取、分析及交易策略

在多资产投资组合的分析框架中,除单资产的收益及波动率等高阶矩外,协偏度以及协峰度等高阶协矩亦是不可忽视的系统性风险度量.本文借鉴Bakshi等(2003)等文献的研究框架,利用台湾期权市场数据提取隐含高阶总矩、隐含协矩和隐含特质矩,探讨其各自对相关已实现矩的预测效果;并进一步构建协矩交易策略.结果表明:相较偏度及峰度,隐含波动率与实际波动率走势及统计特征均更为一致.协偏度、协峰度的波动相比协方差要剧烈得多.引入多市场信息的预测效果要优于单独采用某一市场信息的效果.协矩交易策略方面:历史矩与隐含矩信息在组合构建的差异主要体现在偏度与峰度等更高阶矩上.历史协方差与协偏度在市场趋稳时期表现相对较佳;隐含协矩的优势在于策略构建的稳健性更好.期权市场信息的有效反映取决于市场的成熟、演进及交易活跃度的提升.     

上证50ETF期权隐含波动风险对资本市场风险的预警能力分析

使用上证50ETF期权数据计算隐含波动率风险来刻画"常规"的波动,使用隐含尾部风险刻画非对称的隐含波动风险,构造出了对中国股票市场有显著风险预警能力的风险测度。首先,选取上证50指数和沪深300指数,使用两指数收益率序列的高阶矩作为股市未来的风险度量,用长短国债利差作为宏观风险的代理变量,证实了上证50ETF期权隐含波动率风险和隐含尾部风险对未来6个月内的股票市场风险和宏观风险都有显著预测能力。其次,使用有变点的分位数自回归模型对隐含尾部风险进行建模,并在贝叶斯框架下使用MCMC方法估计出了两个隐含尾部风险的突变日期:2016年3月3日和2017年12月15日。使用以上两个突变日期将股指序列和长短国债利差序列划分为三个时期,发现三个时期内的股票市场风险和宏观风险都有显著的差异。观察差异结果可以发现,当金融市场处于高波动风险时,宏观风险也相应较高,尾部风险呈高分位膨胀性;随着尾部风险的突变发生,金融市场和宏观市场风险开始降低并结束波动期,继而迎来一段时间的稳定上升;当市场一直处于较为稳定的上升状态并伴随着较低的宏观风险时,此时尾部风险逐渐增加并再次发生突变,预示着股票和宏观市场再一次迎来一段波动期。研究证明,期权隐含波动风险对股票市场乃至宏观资本市场都有显著的风险预警能力。     

无模型隐含波动率的信息含量与定价能力——基于上证50ETF期权的实证研究

本文从上证50ETF期权价格中提取无模型隐含波动率并检验其信息含量,基于随机折现因子理论推导波动率风险的系统性与正负性判定公式,从波动率风险溢酬和相关性两方面验证波动率是否为系统性风险,进而基于A股市场的个股数据检验波动率风险在股票截面收益上的定价能力。研究结果表明：无模型隐含波动率包含BS隐含波动率中的所有信息和历史波动率中的大部分信息,是未来已实现波动率的有效估计;市场波动率为系统性风险因子且存在显著为负的风险溢酬;组合分析表明,对市场波动率暴露较大的股票组合在未来的收益较低,且暴露最大与最小股票组合的收益率之差显著为负,该结论在控制经典风险因子和改变交易策略之后依然稳健;Fama-MacBeth两步法结果表明波动率风险被定价且风险价格显著为负。     

中国股市高阶矩风险及其对投资收益的冲击

本文首先建立NAGARCHSK模型,推算市场收益率的条件高阶矩序列,在此基础上建立引入高阶矩风险的收益-风险时变四因子状态空间模型,并基于2000-2016年中国股票市场的收益率数据,实证探究不同时期市场高阶矩风险对投资收益的冲击.结果显示:我国股票市场收益受到高阶矩风险的影响,并且条件高阶矩序列表现出时变和波动聚集的特征,大规模的全球性金融危机和国内市场的重大风险事件均会使股市收益的条件高阶矩序列出现持续的异常波动.在未出现极端金融危机的稳定时期,市场收益率的条件方差会趋于对投资收益产生正向影响,条件偏度和条件峰度对投资收益的影响在正向和负向之间不断交替,增加了投资收益的不确定性.然而在全球性的极端金融危机时期,市场收益率的条件方差会转而对投资收益产生负向影响,条件峰度则会对投资收益带来持续的正向影响.     

基于多目标优化和效用理论的高阶矩动态组合投资

 存在高阶矩风险偏好条件下，组合投资选择必须考虑最大化收益、偏度和最小化方差、峰度四个相互冲突的目标。同时，考虑到高阶矩风险的时变特征，应建立高阶矩动态组合投资模型。基于多目标优化技术和效用理论，讨论了高阶矩动态组合投资模型的构建，并利用MATLAB软件中的非线性优化函数fmincon对模型进行了求解，从理论和实证两个层面对两类模型进行对比。     

基于中国隐含波动率和方差溢价的实证研究

隐含波动率在资本市场中发挥着重要作用,本文使用二次幂变差方法,首次就我国股市的隐含波动率指数及其方差溢价对股市收益和宏观经济活动的预测能力进行实证分析.研究发现:隐含波动率的增加会加剧市场波动风险;方差的连续部分和跳跃部分对未来的实现方差具有显著的正向影响;相对于周收益,方差溢价和波动率指数对月度收益的预测能力更强;隐含波动率指数和方差溢价目前无法对我国宏观经济活动起到预测作用.研究结论为进一步分析我国证券市场的风险偏好提供了经验证据.     

高阶矩CAPM模型的建立及实证分析

本文在传统的CAPM模型中引入系统偏度、系统峰度等高阶矩,发展和推广了CAPM模型,实证分析结果表明高阶矩CAPM模型优于传统CAPM模型.     

投资决策风险把握及其计算方法研究

文章把企业经营价值预测基础的销售额指标作为起点,结合β分布函数,探讨了企业投资项目经营价值的概率分布、高阶距的风险特征值的表示与计量方法,并就其在NPV法与实物期权法具体应用和两者差异进行了对比分析,得到的结论是:实物期权方法在风险管理上的优势是具有更高的自由度,但伴随经营价值概率分布的变化,表征风险的偏度和峰度也随之变化。     

期权市场对现货市场波动率影响的实证分析——基于上证50ETF期权上市前后的比较

上证50ETF期权于2015年2月9日正式推出,这是中国第一只场内期权,对推动中国金融衍生品市场的进一步发展有重要的示范意义。结合ARMA-GARCH模型和TGARCH模型对上证50ETF在期权上市前后现货市场的波动情况进行建模分析,发现上证50ETF收益率的波动在期权上市后平均有所减小,但是在期权上市后的第一年波动率增加,第二年比较小;另一方面上证50ETF的收益率在期权上市后的第一年存在显著的非对称波动现象,但是在第二年不明显。     

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。     

PRICING AUSTRALIAN S&P200 OPTIONS: A BAYESIAN APPROACH BASED ON GENERALIZED DISTRIBUTIONAL FORMS

This paper develops a new class of option price models and applies it to options on the Australian S&P200 Index. The class of models generalizes the traditional Black‐Scholes framework by accommodating time‐varying conditional volatility, skewness and excess kurtosis in the underlying returns process. An important property of these more general pricing models is that the computational requirements are essentially the same as those associated with the Black‐Scholes model, with both methods being based on one‐dimensional integrals. Bayesian inferential methods are used to evaluate a range of models nested in the general framework, using observed market option prices. The evaluation is based on posterior parameter distributions, as well as posterior model probabilities. Various fit and predictive measures, plus implied volatility graphs, are also used to rank the alternative models. The empirical results provide evidence that time‐varying volatility, leptokurtosis and a small degree of negative skewness are priced in Australian stock market options.     

Practical implications of higher moments in risk management

In this paper the out-of-sample prediction of Value-at-Risk by means of models accounting for higher moments is studied. We consider models differing in terms of skewness and kurtosis and, in particular, the GARCHDSK model, which allows for constant and dynamic skewness and kurtosis. The issue of VaR prediction performance is approached first from a purely statistical viewpoint, studying the properties concerning correct coverage rates and independence of VaR violations. Then, financial implications of different VaR models, in terms of market risk capital requirements, as defined by the Basel Accord, are considered. Our results, based on the analysis of eight international stock indexes, highlight the presence of conditional skewness and kurtosis, in some case time-varying, and point out that asymmetry plays a significant role in risk management.     

Distributional properties of continuous time processes: from CIR to bates

In this paper, we compute closed-form expressions of moments and comoments for the CIR process which allows us to provide a new construction of the transition probability density based on a moment argument that differs from the historic approach. For Bates’ model with stochastic volatility and jumps, we show that finite difference approximations of higher moments such as the skewness and the kurtosis are unstable and, as a remedy, provide exact analytic formulas for log-returns. Our approach does not assume a constant mean for log-price differentials but correctly incorporates volatility resulting from Ito’s lemma. We also provide R, MATLAB, and Mathematica modules with exact implementations of the theoretical conditional and unconditional moments. These modules should prove useful for empirical research.

     

基于回归的时变偏度和时变峰度识别检验

资产收益率时变高阶矩建模的首要前提是资产收益率的偏度和峰度具有时变性,即资产收益率存在类似于异方差性的异偏度和异峰度特征。目前文献中的时变偏度和时变峰度识别检验存在适用性较差且检验功效较低等不足。本文提出基于回归的检验方法识别资产收益率偏度和峰度的时变性。该检验一方面利用概率积分变换缓解了拉格朗日乘数检验对资产收益率序列的高阶矩存在性的限制,另一方面考虑了检验统计量中参数估计的不确定性对其统计性质的影响,具有良好的渐近统计性质且适用性更广。蒙特卡洛模拟表明该检验具有良好的有限样本性质,具有合适的检验水平和较高的检验功效。最后,将基于回归的检验运用于上证综指和深圳成指收益率的时变建模研究中。     

A Stochastic Volatility Model With Conditional Skewness

We develop a discrete-time affine stochastic volatility model with time-varying conditional skewness (SVS). Importantly, we disentangle the dynamics of conditional volatility and conditional skewness in a coherent way. Our approach allows current asset returns to be asymmetric conditional on current factors and past information, which we term contemporaneous asymmetry. Conditional skewness is an explicit combination of the conditional leverage effect and contemporaneous asymmetry. We derive analytical formulas for various return moments that are used for generalized method of moments (GMM) estimation. Applying our approach to S&P500 index daily returns and option data, we show that one- and two-factor SVS models provide a better fit for both the historical and the risk-neutral distribution of returns, compared to existing affine generalized autoregressive conditional heteroscedasticity (GARCH), and stochastic volatility with jumps (SVJ) models. Our results are not due to an overparameterization of the model: the one-factor SVS models have the same number of parameters as their one-factor GARCH competitors and less than the SVJ benchmark.     

Skewness,kurtosis, and black-scholes option mispricing

The Black-Scholes option pricing model assumes that (instantaneous) common stock returns are normally distributed. However, the observed distribution exhibits deviations from normality; in particular skewness and kurtosis. We attribute these deviations to gross data errors. Using options' transactions data, we establish that the sample standard deviation, sample skewness, and sample kurtosis contribute to the Black-Scholes model's observed mispricing of a sample from the Berkeley Options Data Base of 2323 call options written on 88 common stocks paying no dividends during the options'life. Following Huber's statement that the primary case for robust statistics is when the shape of the observed distribution deviates slightly from the assumed distribution (usually the Gaussian), we show that robust volatility estimators eliminate the mispricing with respect to sample skewness and sample kurtosis, and significantly improve the Black-Scholes model's pricing performance with respect to estimated volatility.     

Beta estimation in the market model: skewness and leptokurtosis

Leptokurtosis and skewness characterize the distributions of the returns for many financial instruments traded in security markets. These departures from normality can adversely affect the efficiency of least squares estimates of the β's in the single index or market model. The proposed new partially adaptive estimation techniques accommodate skewed and fat tailed distributions. The empirical investigation, which is the first application of this procedure in regression models, reveals that both skewness and kurtosis can affect β estimates.     

股市危机中股指期货应该限制交易吗——基于2015年股市危机的实证分析

利用上证50、沪深300和中证500股指期货合约及其相应指数的高频数据,克服了传统BEKK和DCC模型的不足,通过建立VECM-DCC-VARMA-AGARCH模型考察股市危机期间中国股指期货市场与股票市场之间的信息传导关系与风险传染效应。研究结果表明,股市危机期间股指期货具有很强的价格引导和风险传染效应,股指期货的持续波动加剧了股票市场的进一步波动。因此,提出风险传染效应与市值规模相关、非对称效应和非预期冲击效应与市值规模负相关、波动的风险传染效应与市值规模正相关。危机时期,应抑制股指期货市场上的过度投机,对股指期货采取限制开仓、提高交易保证金和交易手续费都是正确和切实可行的措施。建议监管当局健全股指期货和股票市场交易制度。     

A Standardized Normal-Laplace Mixture Distribution Fitted to Symmetric Implied Volatility Smiles

This article proposes to use a standardized version of the normal-Laplace mixture distribution for the modeling of tail-fatness in an asset return distribution and for the fitting of volatility smiles implied by option prices. Despite the fact that only two free parameters are used, the proposed distribution allows arbitrarily high kurtosis and uses one shape parameter to adjust the density function within three standard deviations for any specified kurtosis. For an asset price model based on this distribution, the closed-form formulas for European option prices are derived, and subsequently the volatility smiles can be easily obtained. A regression analysis is conducted to show that the kurtosis, which is commonly used as an index of tail-fatness, is unable to explain the smiles satisfactorily under the proposed model, because the additional shape parameter also significantly accounts for the deviations revealed in smiles. The effectiveness of the proposed parsimonious model is demonstrated in the practical examples where the model is fitted to the volatility smiles implied by the NASDAQ market traded foreign exchange options.