A Range-Based Multivariate Stochastic Volatility Model for Exchange Rates

In this paper we present a parsimonious multivariate model for exchange rate volatilities based on logarithmic high-low ranges of daily exchange rates. The multivariate stochastic volatility model decomposes the log range of each exchange rate into two independent latent factors, which could be interpreted as the underlying currency specific components. Owing to the empirical normality of the logarithmic range measure the model can be estimated conveniently with the standard Kalman filter methodology. Our results show that our model fits the exchange rate data quite well. Exchange rate news seems to be currency specific and allows identification of currency contributions to both exchange rate levels and exchange rate volatilities.     

上海铜期货日流动性与日波动性关系的实证研究

本文对上海期货交易所铜期货市场的日流动性和波动性进行了实证研究。在考察交易量与波动的关系时借鉴了混合分布假设理论(MDH),而在考察流动性比率与波动性的关系时则在前人基础上建立了新的模型。通过实证得出交易量与波动率有显著的正相关关系的结论。而在考察流动性比率与波动性关系时,却发现二者并没有显著的关系。     

Edgeworth Corrections for Realized Volatility

The quality of the asymptotic normality of realized volatility can be poor if sampling does not occur at very high frequencies. In this article we consider an alternative approximation to the finite sample distribution of realized volatility based on Edgeworth expansions. In particular, we show how confidence intervals for integrated volatility can be constructed using these Edgeworth expansions. The Monte Carlo study we conduct shows that the intervals based on the Edgeworth corrections have improved properties relatively to the conventional intervals based on the normal approximation. Contrary to the bootstrap, the Edgeworth approach is an analytical approach that is easily implemented, without requiring any resampling of one's data. A comparison between the bootstrap and the Edgeworth expansion shows that the bootstrap outperforms the Edgeworth corrected intervals. Thus, if we are willing to incur in the additional computational cost involved in computing bootstrap intervals, these are preferred over the Edgeworth intervals. Nevertheless, if we are not willing to incur in this additional cost, our results suggest that Edgeworth corrected intervals should replace the conventional intervals based on the first order normal approximation.     

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.     

A New Approach to Importance Sampling in Taylor’s Stochastic Volatility Model

This article presents the general analysis of finite high-dimensional integrals using the Importance Sampling (IS) in aim to the parameter estimation of Taylor’s stochastic volatility (SV) model. After we proceed to make an alternative derivation for Sequential Importance Sampling (SIS) in previous literatures, we propose a new approach to select the optimal parameters of sampler, which is called as Universal Importance Sampling (UIS). UIS minimizes the Monte Carlo variance and numerically performs at least the same accurately as the SIS algorithm, but the computational efficiency get greatly improved. We apply both methods and investigate the SV model on the data, then make comparisons of the results.     

股价波动持续性与反转收益

动量效应和反转效应是资本市场的热点话题,学术界给出了诸多解释,但鲜有文献从风险时变性视角关注到波动持续性的影响。基于2005—2021年我国A股市场个股数据,利用GARCH族模型度量股价波动持续性,分别通过投资组合分析与混同横截面分析,实证检验了个股股价波动持续性与股票预期收益之间的关系。研究发现:股价波动持续性与预期收益之间存在显著的负相关关系;通过构建多空组合,在买入波动持续性小的股票的同时卖出波动持续性大的股票,能够获得显著的超额收益。同时,针对我国A股市场存在“反转效应”的特征事实,进一步检验了股价波动持续性对反转收益的影响。经验证据表明,股价波动持续性放大了反转收益。因此,投资者可以通过纳入刻画股价波动持续性与反转效应的因子改善投资组合的业绩;监管部门应加强对股价波动持续性的实时关注,并将其作为系统性风险预警的重点指标。      

波动率偏斜与风险中性偏度能预测尾部风险吗

论文从S＆P 500指数期权数据中提取出波动率偏斜与风险中性偏度指标, 采用Logistic模型研究了波动率偏斜/风险中性偏度是否对未来真实的市场尾部风险具有预测力。结果发现, 波动率偏斜/风险中性偏度仅含有未来市场尾部风险的一定信息, 但并不能准确预测未来市场尾部风险发生的状态。相反, 波动率偏斜/风险中性偏度与投资者情绪指标显著相关。     

中国ETF基金价格“已实现”波动率、跟踪误差之间的Granger关系研究

在高频数据条件下,中国ETF基金价格"已实现"波动率与跟踪误差之间是否存在着因果关系并存在着信息的先导效应？基于"已实现"波动、跟踪误差计算方法及Granger因果检验过程、VAR模型等,本文对此进行了深入研究。研究结果认为:中国ETF基金价格"已实现"波动率与两种跟踪误差分别具有Granger因果关系,后者是前者的Granger原因;中国ETF基金价格"已实现"波动率序列与两种跟踪误差序列的同期及一、二阶滞后相关性较高,而跟踪误差滞后于"已实现"波动率;当ETF基金的跟踪误差受外部市场条件的某一冲击后,将给ETF基金价格"已实现"波动率带来同向的冲击,这一冲击具有一定的持续性和滞后性。     

Some applications of nonlinear and non-Gaussian state–space modelling by means of hidden Markov models

Nonlinear and non-Gaussian state–space models (SSMs) are fitted to different types of time series. The applications include homogeneous and seasonal time series, in particular earthquake counts, polio counts, rainfall occurrence data, glacial varve data and daily returns on a share. The considered SSMs comprise Poisson, Bernoulli, gamma and Student-t distributions at the observation level. Parameter estimations for the SSMs are carried out using a likelihood approximation that is obtained after discretization of the state space. The approximation can be made arbitrarily accurate, and the approximated likelihood is precisely that of a finite-state hidden Markov model (HMM). The proposed method enables us to apply standard HMM techniques. It is easy to implement and can be extended to all kinds of SSMs in a straightforward manner.     

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.