连续贝塔、非连续贝塔与股票风险溢酬

本文利用高频数据将传统的CAPM贝塔分解为连续贝塔和非连续贝塔（跳跃贝塔和隔夜贝塔），并在此基础上进一步考虑正向市场和负向市场的非对称性，将跳跃贝塔又细分为正向跳跃贝塔和负向跳跃贝塔，以探讨不同类型系统性风险的特征差异及其所对应的风险溢酬。实证结果表明，个股对市场发生的非连续变动比连续变动更加敏感，投资者对市场发生的负向跳跃比正向跳跃反应更加强烈；中国股票市场上的系统性非连续风险溢酬（跳跃风险溢酬和隔夜风险溢酬）显著为正，但系统性连续风险并没有得到定价；其中，跳跃风险溢酬则主要来源于对系统性负向跳跃风险的补偿，而正向跳跃风险对股票横截面收益率没有显著的影响。     

Analysis of a jump-diffusion option pricing model with serially correlated jump sizes

This paper extends the classical jump-diffusion option pricing model to incorporate serially correlated jump sizes which have been documented in recent empirical studies. We model the series of jump sizes by an autoregressive process and provide an analysis on the underlying stock return process. Based on this analysis, the European option price and the hedging parameters under the extended model are derived analytically. Through numerical examples, we investigate how the autocorrelation of jump sizes influences stock returns, option prices and hedging parameters, and demonstrate its effects on hedging portfolios and implied volatility smiles. A calibration example based on real market data is provided to show the advantage of incorporating the autocorrelation of jump sizes.     

The Distribution of Stock Returns When the Market Is Up

Abstract

For some investments, the relation between stock returns and the market proxy is conventionally described by a linear regression model with the normality assumption. This paper derives the distribution of stock returns for a security in an upgrade (or downgrade) market with the assumption that the log stock returns of the market proxy follow a mixture of normal distributions. We discuss MLE and the method of moment estimation for parameters involved in the model. An analysis of stock data in Johannesburg Stock Exchange is included to illustrate the model. This note explains the phenomenon in financial analysis regarding the shape of the distribution of long-run stock returns limited on an upgrade or downgrade market index.     

中、印、美股市联动差异性研究

基于扩散视角和跳跃视角探究了中、印、美股市联动行为。基于扩散视角,美国和印度股市与中国股市有明显的单向收益溢出效应,中美之间有明显的波动溢出效应,但是中印之间却不存在这种关系。从非对称影响的结果来看,只存在印度股市和美国股市与中国股市单向的非对称影响。基于跳跃视角,中印、中美股市的平均跳跃幅度和平均方差贡献率,与其跳跃强度相比联动性更高,中印联合跳跃比率相关系数和中美联合跳跃比率相关系数都处于较高水平,同时稳健性检验的结果表明结论整体具有一致性。     

基于熵最大原则的GPD估计与中国股市极值风险测度

POT极值模型参数的准确估计是计算金融资产回报市场风险的关键。根据最大化熵原则（POME）得到POT模型中GPD参数估计方程组,通过回归模型的可决系数法选取阈值,最后将其应用到中国两个时段股市金融风险测度的实证研究中。结果表明：第1、2时段,最优阈值分别为0．01799、0．01801,γ、ξ和β的估计值分别为18．53467、0．14871、0．00802和2．93172、0．03649、0．01258,并得到不同显著性水平下的VaR和ES值,为GPD参数估计找到了一个更科学有效的方法,更为准确计算金融资产回报市场风险提供了新思路,同时也测算了本次国际金融危机对中国股市风险的影响。     

Estimating the Parameters of Stochastic Volatility Models Using Option Price Data

This article describes a maximum likelihood method for estimating the parameters of the standard square-root stochastic volatility model and a variant of the model that includes jumps in equity prices. The model is fitted to data on the S&P 500 Index and the prices of vanilla options written on the index, for the period 1990 to 2011. The method is able to estimate both the parameters of the physical measure (associated with the index) and the parameters of the risk-neutral measure (associated with the options), including the volatility and jump risk premia. The estimation is implemented using a particle filter whose efficacy is demonstrated under simulation. The computational load of this estimation method, which previously has been prohibitive, is managed by the effective use of parallel computing using graphics processing units (GPUs). The empirical results indicate that the parameters of the models are reliably estimated and consistent with values reported in previous work. In particular, both the volatility risk premium and the jump risk premium are found to be significant.     

Testing Alphas in Conditional Time-Varying Factor Models With High-Dimensional Assets

ABSTRACT

For conditional time-varying factor models with high-dimensional assets, this article proposes a high-dimensional alpha (HDA) test to assess whether there exist abnormal returns on securities (or portfolios) over the theoretical expected returns. To employ this test effectively, a constant coefficient test is also introduced. It examines the validity of constant alphas and factor loadings. Simulation studies and an empirical example are presented to illustrate the finite sample performance and the usefulness of the proposed tests. Using the HDA test, the empirical example demonstrates that the FF three-factor model is better than CAPM in explaining the mean-variance efficiency of both the Chinese and U.S. stock markets. Furthermore, our results suggest that the U.S. stock market is more efficient in terms of mean-variance efficiency than the Chinese stock market. Supplementary materials for this article are available online.     

Value-at-risk estimation by LS-SVR and FS-LS-SVR based on GAS model

ABSTRACT

Conditional risk measuring plays an important role in financial regulation and depends on volatility estimation. A new class of parameter models called Generalized Autoregressive Score (GAS) model has been successfully applied for different error's densities and for different problems of time series prediction in particular for volatility modeling and VaR estimation. To improve the estimating accuracy of the GAS model, this study proposed a semi-parametric method, LS-SVR and FS-LS-SVR applied to the GAS model to estimate the conditional VaR. In particular, we fit the GAS(1,1) model to the return series using three different distributions. Then, LS-SVR and FS-LS-SVR approximate the GAS(1,1) model. An empirical research was performed to illustrate the effectiveness of the proposed method. More precisely, the experimental results from four stock indexes returns suggest that using hybrid models, GAS-LS-SVR and GAS-FS-LS-SVR provides improved performances in the VaR estimation.     

Empirical Characteristic Function Estimation and Its Applications

Abstract

This paper reviews the method of model-fitting via the empirical characteristic function. The advantage of using this procedure is that one can avoid difficulties inherent in calculating or maximizing the likelihood function. Thus it is a desirable estimation method when the maximum likelihood approach encounters difficulties but the characteristic function has a tractable expression. The basic idea of the empirical characteristic function method is to match the characteristic function derived from the model and the empirical characteristic function obtained from data. Ideas are illustrated by using the methodology to estimate a diffusion model that includes a self-exciting jump component. A Monte Carlo study shows that the finite sample performance of the proposed procedure offers an improvement over a GMM procedure. An application using over 72 years of DJIA daily returns reveals evidence of jump clustering.     

FIGARCH模型对股市收益长记忆性的实证分析

一、问题的提出长记忆性是指过去的冲击持续到将来,对预期的将来具有很大的影响。在大多数情况下,自相关函数的曲线图用来描述时间序列的长记忆特征。因此长记忆性可以定义如下：假设Ｙｔ是一个离散的时间序列,ｊ阶滞后的自相关函数为ρｊ,如果有ｌｉｍｎ→∞Σｎｊ＝...     

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.     

Efficient and flexible model-based clustering of jumps in diffusion processes

Jump–diffusion processes involving diffusion processes with discontinuous movements, called jumps, are widely used to model time-series data that commonly exhibit discontinuity in their sample paths. The existing jump–diffusion models have been recently extended to multivariate time-series data. The models are, however, still limited by a single parametric jump-size distribution that is common across different subjects. Such strong parametric assumptions for the shape and structure of a jump-size distribution may be too restrictive and unrealistic for multiple subjects with different characteristics. This paper thus proposes an efficient Bayesian nonparametric method to flexibly model a jump-size distribution while borrowing information across subjects in a clustering procedure using a nested Dirichlet process. For efficient posterior computation, a partially collapsed Gibbs sampler is devised to fit the proposed model. The proposed methodology is illustrated through a simulation study and an application to daily stock price data for companies in the S&P 100 index from June 2007 to June 2017.     

Flexible modeling of conditional distributions using smooth mixtures of asymmetric student t densities

A general model is proposed for flexibly estimating the density of a continuous response variable conditional on a possibly high-dimensional set of covariates. The model is a finite mixture of asymmetric student t densities with covariate-dependent mixture weights. The four parameters of the components, the mean, degrees of freedom, scale and skewness, are all modeled as functions of the covariates. Inference is Bayesian and the computation is carried out using Markov chain Monte Carlo simulation. To enable model parsimony, a variable selection prior is used in each set of covariates and among the covariates in the mixing weights. The model is used to analyze the distribution of daily stock market returns, and shown to more accurately forecast the distribution of returns than other widely used models for financial data.     

Ambiguity in the Cross-Section of Expected Returns: An Empirical Assessment

This article estimates and tests the smooth ambiguity model of Klibanoff, Marinacci, and Mukerji based on stock market data. We introduce a novel methodology to estimate the conditional expectation, which characterizes the impact of a decision maker’s ambiguity attitude on asset prices. Our point estimates of the ambiguity parameter are between 25 and 60, whereas our risk aversion estimates are considerably lower. The substantial difference indicates that market participants are ambiguity averse. Furthermore, we evaluate if ambiguity aversion helps explaining the cross-section of expected returns. Compared with Epstein and Zin preferences, we find that incorporating ambiguity into the decision model improves the fit to the data while keeping relative risk aversion at more reasonable levels. Supplementary materials for this article are available online.     

Lattice-oriented percolation system applied to volatility behavior of stock market

In this paper, a discrete time series of stock price process is modeled by the two-dimensional lattice-oriented bond percolation system. Percolation theory, as one of statistical physics systems, has brought new understanding and techniques to a broad range of topics in nature and society. According to this financial model, we studied the statistical behaviors of the stock price from the model and the real stock prices by comparison. We also investigated the probability distributions, the long memory and the long-range correlations of price returns for the actual data and the simulative data. The empirical research exhibits that for proper parameters, the simulative data of the financial model can fit the real markets to a certain extent.     

Optimal investment and life insurance strategies in a mixed jump-diffusion framework

Abstract

This article investigates an optimal investment and life insurance strategies in a mixed jump-diffusion framework. The individual life insurance policyholder who has CRRA preferences. The market consists of riskless asset, a zero-coupon bond, a stock and life insurance. The instantaneous interest rate is modeled as the O-U model, while a zero-coupon bond with credit risk follows a BSDE and a risky asset be driven by MJD-fBm model. The problem is solved by the mixed jump diffusion fractional HJB SDE which satisfied the admissible strategy, then the closed form solution and optimal strategies are derived and the simulation of the various parameters are also given.     

An empirical Bayesian forecast in the threshold stochastic volatility models

In the area of finance, the stochastic volatility (SV) model is a useful tool for modelling stock market returns. However, there is evidence that asymmetric behaviour of stock returns exists. A threshold SV (THSV) model is provided to capture this behaviour. In this study, we introduce a robust model created through empirical Bayesian analysis to deal with the uncertainty between the SV and THSV models. A Markov chain Monte Carlo algorithm is applied to empirically select the hyperparameters of the prior distribution. Furthermore, the value at risk from the resulting predictive distribution is also given. Simulation studies show that the proposed empirical Bayes model not only clarifies the acceptability of prediction but also reduces the risk of model uncertainty.     

Confidence interval of the jump activity index based on empirical likelihood using high frequency data

It is widely accepted that jumps exist in the asset price process. The jump activity index is a natural measure of how frequent the jumps are. Statistical inference of the jump activity index is of importance in determining the type of process that underlies the dynamics of the log price process. In this paper, we implement the empirical likelihood approach to construct the confidence interval of the jump activity index of a pure jump model using high frequency data. Wilks' theorem is established. We also extend the result on Zhao and Wu (2009)'s estimator to the more general framework in this paper. Simulation studies demonstrate the good performance of the empirical likelihood approach. Compared with the existing non-parametric estimator proposed by Zhao and Wu (2009), the empirical likelihood approach gives more accurate coverage probabilities in the simulation studies.     

基于非参数核估计的股市风险理论及应用研究

根据中国股市非市场化特点与股权分置改革的影响等问题,在股票市场价格严重失真情况下,运用非参数核估计方法,拟合了股市的理论收益率指标,通过对比股市实际收益率指标显著性偏离关系,提出了中国股市风险理论的独特含义与计量方法。实证显示：非参数核估计能够很好估计股市理论收益率指标,准确地计量中国股市风险动态变化情况。     

沪深A、B股市场信息传递路径实证分析

运用计量经济学中的ARCH-LM检验、GARCH模型、Granger引导关系检验等分析方法，实证分析了B股市场对境内投资者开放前后沪深两市A指收益率序列与B指收益率序列和非预期收益率序列的Granger引导关系，给出沪深A、B股市场信息传递路径，并且指出从信息流动角度来说，A、B股市场整合的方式是从A股市场向B股市场的内幕消息的传递和从B股市场向A股市场的投资理念的趋同。