Modelling Regime‐Specific Stock Price Volatility*

Single‐state generalized autoregressive conditional heteroscedasticity (GARCH) models identify only one mechanism governing the response of volatility to market shocks, and the conditional higher moments are constant, unless modelled explicitly. So they neither capture state‐dependent behaviour of volatility nor explain why the equity index skew persists into long‐dated options. Markov switching (MS) GARCH models specify several volatility states with endogenous conditional skewness and kurtosis; of these the simplest to estimate is normal mixture (NM) GARCH, which has constant state probabilities. We introduce a state‐dependent leverage effect to NM‐GARCH and thereby explain the observed characteristics of equity index returns and implied volatility skews, without resorting to time‐varying volatility risk premia. An empirical study on European equity indices identifies two‐state asymmetric NM‐GARCH as the best fit of the 15 models considered. During stable markets volatility behaviour is broadly similar across all indices, but the crash probability and the behaviour of returns and volatility during a crash depends on the index. The volatility mean‐reversion and leverage effects during crash markets are quite different from those in the stable regime.     

Do short selling restrictions destabilize stock markets? Lessons from Taiwan

Short sellers have been routinely blamed for triggering, or exacerbating, stock market declines. The experience of Taiwan provides an interesting case study of the impact of short selling bans on stock returns volatility in a time series framework due to the length of time the short selling ban was in place there. Estimating several variants of an asymmetric GARCH model and a Markov switching GARCH model we find robust evidence that short selling restrictions raise stock returns volatility. The only qualifier is that the impact of short sale bans is a feature of the expansionary phase of business cycles. During recessions this effect dissipates.     

Improving the realized GARCH’s volatility forecast for Bitcoin with jump-robust estimators

This study employs the realized GARCH (RGARCH) model to estimate the volatility of Bitcoin returns and measure the benefits of various scaled realized measures in forecasting volatility. Empirical results show that considerable price jumps occurred in the Bitcoin market, suggesting that a jump-robust realized measure is crucial to estimate Bitcoin volatility. The RGARCH model, especially the one with tri-power variation, outperforms the standard GARCH model. Additionally, the RGARCH model with jump-robust realized measures can provide steady forecasting performance. This study is timely given that the CME may release a Bitcoin option product and our results are relevant to option pricing     

Anticipating Long‐Term Stock Market Volatility

We investigate the relationship between long‐term US stock market risks and the macroeconomic environment using a two‐component GARCH‐MIDAS model. Our results show that macroeconomic variables are important determinants of the secular component of stock market volatility. Among the various macro variables in our dataset the term spread, housing starts, corporate profits and the unemployment rate have the highest predictive ability for long‐term stock market volatility. While the term spread and housing starts are leading variables with respect to stock market volatility, for industrial production and the unemployment rate expectations data from the Survey of Professional Forecasters regarding the future development are most informative. Copyright © 2014 John Wiley & Sons, Ltd.     

基于GARCH模型的股票市场价格波动分析

在经济和金融研究中,波动性一直是一个非常重要的方面,中国股票市场建立至今,股市大起大落成为一种常态。本文建立了上证综合指数波动的GARCH模型,从实证角度说明了上证综合指数波动存在着波动集簇性,而GARCH模型可以很好的拟合股指波动情况,同时对股指收益率也能进行较好的预测,最后根据结论提出了一些对策建议。     

Forecasting volatility with component conditional autoregressive range model

In this paper, we propose a component conditional autoregressive range (CCARR) model for forecasting volatility. The proposed CCARR model assumes that the price range comprises both a long-run (trend) component and a short-run (transitory) component, which has the capacity to capture the long memory property of volatility. The model is intuitive and convenient to implement by using the maximum likelihood estimation method. Empirical analysis using six stock market indices highlights the value of incorporating a second component into range (volatility) modelling and forecasting. In particular, we find that the proposed CCARR model fits the data better than the CARR model, and that it generates more accurate out-of-sample volatility forecasts and contains more information content about the true volatility than the popular GARCH, component GARCH and CARR models.     

我国沪、深股市的波动性研究——基于GARCH族模型

金融市场的波动性不仅是投资者关注的焦点之一,而且也是被研究的热点之一。中国股市还非常年轻,股票市场的价格常常表现出大幅波动的特征。本研究以上证综合指数和深圳成分指数为研究对象,分别运用GARCH模型、TARCH模型和EGARCH模型同时拟合,并对比分析了中国股市日收益率波动的动态特征;结果显示,EGACH模型能更有效拟合股市的波动性。     

The political uncertainty and stock market behavior in emerging democracy: the case of Taiwan

This paper examines the congressional effect between the pre- and post-democratization on the stock market by the asymmetric Generalized Autoregressive Conditional Heterosce desticity (GARCH) model in the period 1984–2004. The results found that the congressional effect is negative effect on stock returns but volatility is not significant. However, the democratic effect on stock returns is negative and increased of volatility. Moreover, the congressional effect on stock market returns following democratization significantly exceeds that before democratization, but have no significant effect for the volatility in the same circumstances. These results provide evidences consistent with the contention of liberalization (Hayek, Am. Econ. Rev. 35, 519–530, Individualism and Economic order, The university of Chicago press, Chicago, London, 1945, 1948; Popper, The open society and its Enemies, Princeton university, NJ, 1950).     

Is there a risk–return trade‐off? Evidence from high‐frequency data

This paper examines the intertemporal relation between risk and return for the aggregate stock market using high‐frequency data. We use daily realized, GARCH, implied, and range‐based volatility estimators to determine the existence and significance of a risk–return trade‐off for several stock market indices. We find a positive and statistically significant relation between the conditional mean and conditional volatility of market returns at the daily level. This result is robust to alternative specifications of the volatility process, across different measures of market return and sample periods, and after controlling for macro‐economic variables associated with business cycle fluctuations. We also analyze the risk–return relationship over time using rolling regressions, and find that the strong positive relation persists throughout our sample period. The market risk measures adopted in the paper add power to the analysis by incorporating valuable information, either by taking advantage of high‐frequency intraday data (in the case of realized, GARCH, and range volatility) or by utilizing the market's expectation of future volatility (in the case of implied volatility index). Copyright © 2006 John Wiley & Sons, Ltd.     

Capturing the volatility smile of options on high-tech stocks—A combined GARCH-neural network approach

A slight modification of the standard GARCH equation results in a good modeling of historical volatility. Using this generated GARCH volatility together with the inputs: spot price divided by strike, time to maturity, and interest rate, a generated Neural Network results in significantly better pricing performance than the Black Scholes model. A single Neural Network for each individual high-tech stock is able to adapt to the market inherent volatility distortion. A single Network for all tested high-tech stocks also results in significantly better pricing performance than the Black-Scholes model. Dr. Gunter Meissner (gmeissner@hawaii.rr.com) is president of Derivatives Software, www.dersoft.com, and associate professor of finance at the Hawaii Pacific University; Noriko Kawano, MSIS, is currently working as a software engineer at Hawaii Dental Service. The article was presented at the eighth Asia Pacific Finance Conference, Shanghai, July 2000.     

基于波动效应与价格发现的期指仿真交易研究

沪深300股指期货仿真交易的推出,对我国现货市场的影响如何以及这种影响是否有利于现货效率的改进。首次采用修正的GARCH模型和向量误差修正模型(VEC)将股指期货推出后现货市场波动性的变化和股指期货与现货市场的价格发现功能结合起来进行对比研究。结果表明,期指仿真交易的推出对于现货市场效率的改进确实存在正面的影响。其引入在短期内加大了现货市场的波动,但这一波动正是市场信息流动加速的反映,因而提高了市场信息的传递效率。同时期货价格领先于现货价格,存在由期货市场到现货市场长期的单向因果关系,说明期货价格具有引导现货价格向均衡方向调整的功能,从而在经验上支持了股指期货市场的开放政策。     

The market for crash risk

This paper examines the equilibrium when stock market crashes can occur and investors have heterogeneous attitudes towards crash risk. The less crash averse insure the more crash averse through options markets that dynamically complete the economy. The resulting equilibrium is compared with various option pricing anomalies: the tendency of stock index options to overpredict volatility and jump risk, the Jackwerth [Recovering risk aversion from option prices and realized returns. Review of Financial Studies 13, 433–451] implicit pricing kernel puzzle, and the stochastic evolution of option prices. Crash aversion is compatible with some static option pricing puzzles, while heterogeneity partially explains dynamic puzzles. Heterogeneity also magnifies substantially the stock market impact of adverse news about fundamentals.     

变结构门限t-GARCH模型及其伪持续性研究

为了反映金融时间序列的波动集聚性、非对称性、厚尾性以及在实证研究中表现出的伪持续性，本文结合门限GARCH模型以及变结构的方法提出了变结构门限t—GARCH模型。首先用Monte Carlo模拟的方法考虑了变结构GARCH模型中存在的伪持续性问题；其次针对金融时间序列非对称性、厚尾性以及强持续性的特点提出了变结构门限t—GARCH模型，总结了关于变结构点检验的几个主要方法；最后用该模型来拟合沪市和深市两个股市的周收益率序列，得到了比GARCH模型更好的拟合结果。     

Sudden equity price declines and the flight-to-safety phenomenon: additional evidence using daily data

Using daily data we show sudden, extreme declines in the U.S. stock market for crash dates to lead to a capital preserving (as opposed to strategic or tactical) reallocation to government debt securities. In most cases we find flight-induced reallocation reverses direction within one day of a crash. However, for the 1987 world crash we find increased and persistent return volatility in both equity and bond returns lasting up to five days following this dramatic decline in world equity prices. Like previous research in this area, we find equity crashes alter long-run stock/bond return correlations and lead to increased stock and bond return volatility. Finally, we describe the somewhat unique stock and bond correlation adjustments triggered by the 9/11 attack and the impact this event had on the behavior of U.S. equity investors?? flight-to-safety reaction.     

Forecasting VIX using two-component realized EGARCH model

In this paper, we propose the two-component realized EGARCH (REGARCH-2C) model, which accommodates the high-frequency information and the long memory volatility through the realized measure of volatility and the component volatility structure, to forecast VIX. We obtain the risk-neutral dynamics of the REGARCH-2C model and derive the corresponding model-implied VIX formula. The parameter estimates of the REGARCH-2C model are obtained via the joint maximum likelihood estimation using observations on the returns, realized measure and VIX. Our empirical results demonstrate that the proposed REGARCH-2C model provides more accurate VIX forecasts compared to a variety of competing models, including the GARCH, GJR-GARCH, nonlinear GARCH, Heston–Nandi GARCH, EGARCH, REGARCH and two two-component GARCH models. This result is found to be robust to alternative realized measure. Our empirical evidence highlights the importance of incorporating the realized measure as well as the component volatility structure for VIX forecasting.     

交易量适合作为股价波动信息的代理变量吗?——来自中国沪深股市的证据

本文利用中国沪深股市日交易数据,采用多元GARCH模型从信息传递的角度进行实证研究,结果表明:股价对交易量具有显著的波动溢出效应,但交易量对股价的波动溢出效应不明显。这种波动的单向溢出说明在应对信息的冲击上股价比交易量能更快地做出反应,其后才通过波动溢出在交易量上得到反映,股价波动对成交量波动具有先导作用。因此,从波动冲击传导和信息传递的角度看,单纯地将交易量视为股价变动信息的代理变量还缺乏稳健的统计证据。     

The dynamic impact of oil price shocks on the stock market and the USD/RMB exchange rate: Evidence from implied volatility indices

Using daily data from March 16, 2011, to September 9, 2019, we explore the dynamic impact of the oil implied volatility index (OVX) changes on the Chinese stock implied volatility index (VXFXI) changes and on the USD/RMB exchange rate implied volatility index (USDCNYV1M) changes. Through a TVP-VAR model, we analyse the time-varying uncertainty transmission effects across the three markets, measured by the changes in implied volatility indices. The empirical results show that the OVX changes are the dominant factor, which has a positive impact on the USDCNYV1M changes and the VXFXI changes during periods of important political and economic events. Moreover, USDCNYV1M changes are the key factor affecting the impact of OVX changes on VXFXI changes. When the oil crisis, exchange rate reform, and stock market crash occurred during 2014–2016, the positive effects of uncertainty transmission among the oil market, the Chinese stock market, and the bilateral exchange rate are significantly strengthened. Finally, we find that the positive effects are significant in the short term but diminish over time.     

Stock returns and volatility: Evidence from the Athens Stock market index

This paper investigates the volatility of the Athens Stock excess stock returns over the period 1990–1999 through the comparison of various conditional hetero-skedasticity models. The empirical results indicate that there is significant evidence for asymmetry in stock returns, which is captured by a quadratic GARCH specification model, while there is strong persistence of shocks into volatility.     

The 1986–88 stock market: Investor sentiment or fundamentals?

This paper tests the widely held proposition that investor sentiment contributed to the stock market crash of 1987. Using weekly data during the 1986–8 period and conventional measures of stock fundamentals, changes in fundamentals are found to have a statistically significant influence on the movement of stock prices. In addition, a much-discussed measure of investor sentiment is used to test the proposition that investor sentiment contributed to the stock market crash of 1987. However, insignificant results regarding the investor sentiment index suggest that either the recently proposed sentiment index is faulty or investor sentiment did not significantly influence stock prices in the period surrounding the 1987 crash.