Properties of the Sample Autocorrelations of Nonlinear Transformations in Long-Memory Stochastic Volatility Models

The autocorrelations of log-squared, squared, and absolute financialreturns are often used to infer the dynamic properties of theunderlying volatility. This article shows that, in the contextof long-memory stochastic volatility models, these autocorrelationsare smaller than the autocorrelations of the log volatilityand so is the rate of decay for squared and absolute returns.Furthermore, the corresponding sample autocorrelations couldhave severe negative biases, making the identification of conditionalheteroscedasticity and long memory a difficult task. Finally,we show that the power of some popular tests for homoscedasticityis larger when they are applied to absolute returns.     

Periodic Stochastic Volatility and Fat Tails

This article provides a comprehensive analysis of the size andstatistical significance of the day of the week, month of theyear, and holiday effects in daily stock index returns and volatility.We employ data from the Dow Jones Industrial Average (DJIA),the S&P 500, the S&P MidCap 400, and the S&P SmallCap600 in order to test whether the seasonal patterns of mediumand small firms are similar to those of large firms. Using formalhypothesis tests based on bootstrapping, we demonstrate thatthere are more significant calendar effects in volatility thanin expected returns, especially for the two large cap indices.More importantly, we introduce the periodic stochastic volatility(PSV) model for characterizing the observed seasonal patternsof daily financial market volatility. We analyze the interactionbetween seasonal heteroskedasticity and fat tails by comparingthe performance of Gaussian PSV and fat-tailed PSVt specificationsto the plain vanilla SV and SVt benchmarks. Consistent withour model-free results, we find strong evidence of seasonalperiodicity in volatility, which essentially eliminates theneed for a fat-tailed conditional distribution, and is robustto the exclusion of the crash of 1987 outliers.     

Mortgage Termination: An Empirical Hazard Model with a Stochastic Term Structure

Pricing for mortgage and mortgage-backed securities is complicated due to the stochastic and interdependent nature of prepayment and default risks. This paper presents a unified economic model of the contingent claims and competing risks of mortgage termination by prepayment and default. I adopt a proportional hazard framework to analyze these competing and interdependent risks in a model with time-varying covariates. The paper incorporates a stochastic interest rate model into the hazard function for prepayment. The empirical results reported in the paper provide new evidence about the ruthlessness of default and prepayment behavior and the sensitivity of these decisions to demographic as well as financial phenomena. The results also illustrate that evaluating the interest rate contingent claims with a stochastic term structure has effects on predicting not only the mortgage prepayment behavior but also the mortgage default behavior.     

Kernel Conditional Quantile Estimation for Stationary Processes with Application to Conditional Value-at-Risk

The paper considers kernel estimation of conditional quantilesfor both short-range and long-range-dependent processes. Undermild regularity conditions, we obtain Bahadur representationsand central limit theorems for kernel quantile estimates ofthose processes. Our theory is applicable to many price processesof assets in finance. In particular, we present an asymptotictheory for kernel estimates of the value-at-risk (VaR) of themarket value of an asset conditional on the historical informationor a state process. The results are assessed based on a smallsimulation and are applied to AT&T monthly returns.     

基于随机波动率假设的权证定价理论评述

随机波动率(SV)模型在衍生品定价和风险管理中的应用开始发挥越来越重要的作用,但是,由于很难得到似然函数的闭型表达式,SV模型的参数估计问题严重限制了它在金融实践领域的普及应用。不过,近年来,学者们提出了许多旨在解决SV模型参数估计问题的有效且可行的新方法,大大推进了SV模型的应用化进程。本文将在权证定价分析的框架内,重点评述SV模型的参数估计方法,并从理论和实证的角度对它们的优点和不足进行简要评介和比较。     

The Stochastic Volatility of Short-Term Interest Rates: Some International Evidence

This paper estimates a stochastic volatility model of short-term riskless interest rate dynamics. Estimated interest rate dynamics are broadly similar across a number of countries and reliable evidence of stochastic volatility is found throughout. In contrast to stock returns, interest rate volatility exhibits faster mean-reverting behavior and innovations in interest rate volatility are negligibly correlated with innovations in interest rates. The less persistent behavior of interest rate volatility reflects the fact that interest rate dynamics are impacted by transient economic shocks such as central bank announcements and other macroeconomic news.     

基于随机波动率假设的权证定价理论评述

随机波动率(SV)模型在衍生品定价和风险管理中的应用开始发挥越来越重要的作用,但是,由于很难得到似然函数的闭型表达式,SV模型的参数估计问题严重限制了它在金融实践领域的普及应用.不过,近年来,学者们提出了许多旨在解决SV模型参数估计问题的有效且可行的新方法,大大推进了SV模型的应用化进程.本文将在权证定价分析的框架内,重点评述SV模型的参数估计方法,并从理论和实证的角度对它们的优点和不足进行简要评介和比较.     

Volatility Implied by Option Prices: The Case of Takeover Bids

We model the effect of an impending share price jump on the implied standard deviation (ISD) of a company's options, testing the model by investigating its predictive ability for ISDs of companies subject to a takeover bid. Our model fits the observed ISDs well for all but certain deep in-the-money options. However, the model demonstrates that a discontinuity in the relationship between moneyness and the ISD both explains the combination of high and zero ISDs exhibited by these options, and impairs the predictive power of the model at these levels of moneyness.     

Modelling the Stochastic Dynamics of Volatility for Equity Indices

The paper develops a class of continuous timestochastic volatility models, which generate asset price returnsthat are approximately Student t distributed. Using thecriterion of local risk minimisation in an incomplete marketsetting, option prices are computed. It is shown that impliedvolatility smile and skew patterns of the type often observed inthe markets can be obtained from this class of stochasticvolatility models.     

Testing for Serial Correlation in the Presence of Stochastic Volatility

This paper develops a regression-based testing procedure for serial correlation in the presence of stochastic volatility. The asymptotic distribution of the test is derived, and the finite sample properties are investigated. Monte Carlo results shows that the test is reliable in terms of both size and power performances, when the underlying process is a log-linear stochastic volatility. Moreover, the test is superior to Woolridge's (1991) robust LM tests in terms of size in finite sample. Serial correlation tests were conducted for nominal returns of ten exchange rates, and indicated that there is a strong evidence of serial correlation for Yen/Dollar exchange rates.     

开放经济下随机折现因子对经济周期与经济波动的解释能力

本文通过研究随机折现因子(SDF)与经济周期以及经济波动的关系,旨在探索金融市场与宏观经济的内在联系。我们构建了一个开放经济定价模型(OEAP model),将汇率、通货膨胀率、国内消费以及市场收益率纳入统一的框架内,探讨SDF对经济周期及经济波动的解释能力。基于模型的估计结果表明在开放经济的模型假设下SDF具有显著的反周期特点并且SDF的波动性方差可以作为衡量经济波动一个很好的指标。另外,模型的模拟结果表明,相对于封闭经济假设下的Epstein-Zin模型,OEAP模型对消费具有更好的拟合效果。这说明OEAP模型对SDF具有更准确的估计。     

Volatility dependences of stock markets with structural breaks

We develop a Vector Heterogeneous Autoregression model with Continuous Volatility and Jumps (VHARCJ) where residuals follow a flexible dynamic heterogeneous covariance structure. We employ the Bayesian data augmentation approach to match the realised volatility series based on high-frequency data from six stock markets. The structural breaks in the covariance are captured by an exogenous stochastic component that follows a three-state Markov regime-switching process. We find that the stock markets have higher volatility dependence during turmoil periods and that breakdowns in volatility dependence can be attributed to the increase in market volatilities. We also find positive correlations between the Asian stock markets, the European stock market, and the UK stock market. The US stock market has positive correlations with all other markets for most of the sample periods, indicating the leading position of US stock market in the global stock markets. In addition, the proposed three-state VHARCJ model with Dynamic Conditional Correlation (DCC) and break structure under student-t distribution has a superior density forecast performance as compared to the competing models. The forecast models with structural breaks outperform those without structural breaks based on the log predicted likelihood, the log Bayesian factor, and the root mean square loss function.     

基于贝叶斯MSSV-ST金融波动模型的股市特征及机制转移性研究

针对有偏厚尾金融随机波动模型难以刻画参数的动态时变性及结构突变的问题,设置偏态参数服从 Markov 转换过程,采用贝叶斯方法,构建带机制转移的有偏厚尾金融随机波动模型,考量股市不同波动状态间的机制转移性,捕捉股市间多重波动特性。通过设置先验分布,实现模型的贝叶斯推断,设计相应的马尔科夫链蒙特卡洛算法进行估计,并利用上证指数进行实证。结果表明：模型不仅刻画了股市的尖峰厚尾、杠杆效应等特性,发现收益率条件分布的偏度参数具有动态时变性,股市波动呈现出显著的机制转移特性,而且证实了若模型考虑波动的不同阶段性状态后,将降低持续性参数向上偏倚幅度的结论。     

The Predictive Power of the French Market Volatility Index: A Multi Horizons Study

The main purpose of this paper is to examine empirically the time series properties of the French Market Volatility Index (VX1). We also examine the VX1's ability to forecast future realized market volatility and finds a strong relationship. More importantly, we show how the index can be used to generate volatility forecasts over different horizons and that these forecasts are reasonably accurate predictors of future realized volatility.     

Capital Asset Pricing Model and Stochastic Volatility: A Case Study of India

The existing literature demonstrates that under a general equilibrium model, the performance of the Capital Asset Pricing Model (CAPM) can be improved significantly by using conditional consumption and market return volatilities as factors. This article tests the validity of these factors explaining stock return differences using a less developed country (India) as a case study. While the earlier studies used panel data to test CAPM, we use portfolios sorted by size and book-to-market equity (BE/ME) ratio. We found that conditional volatility has a limited effect on firms with large capitalization but a significant impact on small-growth and small-value firms.     

Aggregation of Nonparametric Estimators for Volatility Matrix

An aggregated method of nonparametric estimators based on time-domainand state-domain estimators is proposed and studied. To attenuatethe curse of dimensionality, we propose a factor modeling strategy.We first investigate the asymptotic behavior of nonparametricestimators of the volatility matrix in the time domain and inthe state domain. Asymptotic normality is separately establishedfor nonparametric estimators in the time domain and state domain.These two estimators are asymptotically independent. Hence,they can be combined, through a dynamic weighting scheme, toimprove the efficiency of volatility matrix estimation. Theoptimal dynamic weights are derived, and it is shown that theaggregated estimator uniformly dominates volatility matrix estimatorsusing time-domain or state-domain smoothing alone. A simulationstudy, based on an essentially affine model for the term structure,is conducted, and it demonstrates convincingly that the newlyproposed procedure outperforms both time- and state-domain estimators.Empirical studies further endorse the advantages of our aggregatedmethod.     

中国与"一带一路"沿线国家出口贸易研究——基于汇率变动、外贸依存度的视角

引入汇率变动引力模型,采用“一带一路”沿线64个国家2002-2015年面板数据,研究汇率变动和外贸依存度对出口贸易的影响,结果显示：汇率变动不是影响中国对“一带一路”沿线国家出口贸易的最重要因素,人民币升值促进了出口贸易,原因在于中国“一带一路”沿线国家的汇率变动不是很大;外贸依存度对出口贸易影响显著且存在双重门槛效应,外贸依存度越小,出口潜力越大;两国之间距离对出口贸易有显著负向影响;缔结自由贸易协定对出口贸易的影响尚未显现。因此,我国应保持人民币汇率基本稳定,以外贸依存度大小分类实施不同贸易政策,继续推进“一带一路”国家基础设施建设,并细化自由贸易协定。     

The Valuation of Volatility Options

This paper examines the valuation of European- and American-style volatilityoptions based on a general equilibrium stochastic volatility framework.Properties of the optimal exercise region and of the option price areprovided when volatility follows a general diffusion process. Explicitvaluation formulas are derived in four particular cases. Emphasis is placedon the MRLP (mean-reverting in the log) volatility model which has receivedconsiderable empirical support. In this context we examine the propertiesand hedging behavior of volatility options. Unlike American options,European call options on volatility are found to display concavity at highlevels of volatility.