Research on modeling and forecasting of the volatility of securities: a literature review
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    Research on modeling and forecasting of the volatility of securities: a literature review
    Chenggang Li1, 2, Di Wang1, Min Li1, Kang Pan1, Bing Yang1
    1. Faculty of Finance, Guizhou University of Finance and Economics, Guiyang, 550025, Guizhou Province, P. R. China;
    2. Faculty of Science, National University of Singapore, 117546, Singapore

    First Author: Chenggang Li, associate professor, doctor, Faculty of Finance, Guizhou University of Finance and Economics.
    Corresponding Author: Di Wang, Faculty of Finance, Guizhou University of Finance and Economics, Guiyang, 550025, P. R. China, Email:
    Abstract: The stock volatility modeling and forecasting is one of the important problems of practice and academic circles. The circle of theory and practice conducted in-depth research on the stock volatility modeling and forecasting, created a lot of research results. This paper summarized the related research achievements of the stock volatility modeling and forecasting, and pointed out the need to study some of the problems in the future.
    Key words: Securities; Volatility; Modeling; Forecast
        In the securities market investment, investors ( including institutional investors and individual investors ) should not only pay attention to the yield of securities, but also pay attention to the risk of securities. The measurement, analysis and evaluation of securities risk is the important content of the investors in securities market. Among them, the characterization of the volatility of securities returns is the focus of securities risk analysis. Accurately describe the risk and volatility of securities is the core content of risk management, derivative product pricing, asset portfolio construction and securities investment strategy analysis. Therefore, the modeling and prediction of securities volatility has important theoretical and practical significance for the derivatives pricing, measurement of financial risk, government related departments and risk management of securities investors.
    2Security volatility modeling
    There have been a lot of literatures on econometric analysis studying on security volatility modeling. These literatures forecasting security volatility mainly use the following types of models and methods:
    Firstly, some scholars used the autoregressive conditional heteroskedasticity (ARCH) model and the generalized autoregressive conditional heteroskedasticity (GARCH) model proposed by Engle (1982) [1] and Bollerslev (1986) [2] respectively to expand the financial assets volatility modeling and forecasting. Rapach and Strauss (2008) [3], Engle and Rangel (2008) [4], McMillan and Garcia (2009) [5], Drakos et al (2010) [6] also discussed the nature or character of GARCH class models. Their studies concluded that, GARCH type models can well fit and forecast the volatility of return. In recent studies, Efimova and Serletis (2014) [7] investigated the empirical properties of oil, natural gas, and electricity price volatilities using a range of univariate and multivariate GARCH models. Sidorov et al (2014) [8] emphasize on assessing the added value of using news analytics data in improving the explanatory power of the GARCH-Jump model.
    Secondly, some scholars used the Stochastic volatility (SV) model to predict the return volatility and compared the predictive ability of SV models and the GARCH type models. The research results of Omori et al (2007) [9] and Todorov (2010) [10] show that, SV model can better characterize the volatility of return, and its predictive power were better than the GARCH type models. Triantafyllopoulos (2012) [11] proposed a new multi-variate stochastic volatility estimation procedure for financial time series. They considered a Wishart autoregressive process for the volatility precision covariance matrix. Langrock et al (2015) [12] introduced a novel maximum penalized likelihood approach for estimating the conditional distribution in an SV model in a nonparametric way, thus avoiding any potentially critical assumptions on the shape. They considered framework exploits the strengths both of the hidden Markov model machinery and of penalized B-splines, and constituted a powerful alternative to recently developed Bayesian approaches to semiparametric SV modelling.
    Thirdly, some scholars used the realized volatility (RV) model based on high frequency return data to do volatility prediction research. The latest research see Andersen et al (2011) [13], Zhang et al (2011) [14]. Their research showed that the use of realized volatility based on trading day's high-frequency return data as daily volatility measure would greatly reduce the impact of the measurement error and noise on the real volatility process.
    Fourthly, other scholars used the implied volatility (IV) model, derived from the options data, working backwards from the option price to the market’s expectation on future volatility. Dotsis et al (2007) [15], Bollerslev et al (2011) [16] and other studies have shown that implied volatility model had a superiority on volatility modeling and forecasting in the options market. Manela and Moreira (2017) [17] constructed a news implied volatility model (NVIX) to measure the uncertainty starting in 1890 using front-page articles of the Wall Street Journal. They found that News implied volatility (NVIX) peaked during stock market crashes, times of policy-related uncertainty, world wars and financial crises. In US post-war data, periods when NVIX was high were followed by periods of above average stock returns, even after controlling for contemporaneous and forward-looking measures of stock market volatility.
    3Security volatility forecasting
        Many scholars also made some useful discussion on modeling and forecasting volatility. Using GARCH class models, Wang and Li (2005) [18] disscussed exchange return volatility forecasting in detail. He found that different GARCH models’ forecast effects of different exchanges return volatility is different. Huang and Zhong (2007) [19] evaluated the volatility forecasting effects of GARCH class models, and their empirical results showed that either in sample or out of sample, GARCH class models can well forecast the Shanghai Stock Index return volatility. However, the research results of Wei and Yu (2007) [20] showed that, the forecast accuracy of GARCH model was significantly lower than the realized volatility model based on high-frequency data. Zhou’ (2009) [21] study suggested that by realized volatility as the standard, the predictive effect of GARCH class models was not optimistic. Zheng and Huang (2010) [22] used GARCH model and implied volatility model to predict the Hong Kong Hang Seng Index Options volatility, and the empirical analysis results found the prediction ability of GARCH model was better in forecasting one future week’s volatility than the implied volatility model, but implied volatility model performed better in forecasting one future month’s volatility. Taking Shanghai and Shenzhen 300 Index futures mock trading as example, using high frequency data, Wei (2010) [23] compared several types of GARCH models and the RV model, and used Superior Predictive Ability Test Method to test the prediction effects. The empirical results showed that the predictive ability of RV model was obvious better than traditional GARCH class models, and the GARCH models can not better characterize and predict the volatility of the Shanghai and Shenzhen 300 stock index futures. The above scholars’ researches provide a wealth of empirical evidence for further deeply study on the volatility of financial asset returns and risk characteristics.
    4Concluding remarks
    There are many literature studying the security volatility modeling and forecasting. It should be noted that for the existing research, there are still some deficiencies and worthy of further study. Firstly, most existing studies only use univariate GARCH model to model and forecast volatility; secondly, whether using GARCH type models, or using SV model or RV model, most existing studies use low-frequency data (daily data). Using high-frequency data is relatively few; Thirdly, existing studies are only using a variable, return’s information to forecast volatility, without considering other information other than return’s information. Also, there is no explaining the reasons for changes in volatility and impact variables.
    However, Becker and Clements’s (2010) [24] studies suggest that volatility reflects the information shocks contained in trading volume, trading frequency or order flow (order imbalance). Chan and Fong’s (2006) [25] study found that the number of transactions is the main explanatory variable for return volatility. In the interpretation of volatility changes, trading volume and order flow are as well as important with the number of transactions. Based on Kyle’s model, Berger et al (2009) [26] linked volatility changes with order flow and market sensitivity to order flow. The theoretical model and empirical results showed that order flow had strong explanatory power for volatility changes. Meanwhile, liquidity and order flow significantly impact return, and have rich information content. They reflect the flow of funds, and contain information on investors’ buying and selling.
    Based on the above understanding, in order to overcome the defect of past scholars using only one variable, return’s information to model and forecast the return volatility, scholars can uses high-frequency data, and construct Multivariate GARCH models including variables including liquidity, order flow and return to further study the security volatility modeling and forecasting.
    [1] R. F. Engle. Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. Inflation [J]. Econometrica, 1982, 50(4): 987-1008.
    [2] T. Bollerslev. Generalized autoregressive conditional heteroskedasticity [J]. Journal of Econometrics, 1986, 31(3): 307-327.
    [3] D. E. Rapach, J. K. Strauss. Structural breaks and GARCH models of exchange rate volatility [J]. Journal of Applied Econometrics, 2008, 23(1): 65-90.
    [4] R. F. Engle, J. G. Rangel. The spline-GARCH model for low-frequency volatility and its global macroeconomic causes [J]. Review of Financial Studies, 2008, 21(3): 1187-1222.
    [5] D. G. McMillan, R. Q. Garcia. Intra-day volatility forecasts [J]. Applied Financial Economics, 2009, 19(8): 611-623.
    [6] A. A. Drakos, G. P. Kouretas, L. P. Zarangas. Forecasting financial volatility of the Athens stock exchange daily returns: an application of the asymmetric normal mixture GARCH model [J]. International Journal of Finance & Economics, 2010, 15(4): 331-350.
    [7] O. Efimova, A. Serletis. Energy markets volatility modelling using GARCH [J]. Energy Economics, 2014, 43: 264-273.
    [8] S. P. Sidorov, A. Revutskiy, A. Faizliev, et al. Stock Volatility Modelling with Augmented GARCH Model with Jumps [J]. International Journal of Applied Mathematics. 2014, 44(4): 212-220.
    [9] Y. Omori, S. Chib, N. Shephard. Stochastic volatility with leverage: Fast and efficient likelihood inference [J]. Journal of Econometrics, 2007, 140(2): 425-449.
    [10] V. Todorov. Variance Risk-Premium Dynamics: The Role of Jumps [J]. Review of Financial Studies, 2010, 23(1): 345-383.
    [11] K. Triantafyllopoulos. Multi-variate stochastic volatility modelling using Wishart autoregressive processes [J]. Journal of Time Series Analysis, 2012, 33(1): 48-60.
    [12] R. Langrock, T. Michelot, A. Sohn, et al. Semiparametric stochastic volatility modelling using penalized splines [J]. Computational Statistics, 2015, 30(2): 517-537.
    [13] T. G. Andersen, T. Bollerslev, N. Meddahi. Realized volatility forecasting and market microstructure noise [J]. Journal of Econometrics, 2011, 160(1): 220-234.
    [14] L. Zhang, P. A. Mykland, Y. Ait-Sahalia. Edgeworth expansions for realized volatility and related estimators [J]. Journal of Econometrics, 2011, 160(1): 190-203.
    [15] G. Dotsis, D. Psychoyios, G. Skiadopoulos. An empirical comparison of continuous-time models of implied volatility indices [J]. Journal of Banking & Finance, 2007, 31(12): 3584-3603.
    [16] T. Bollerslev, M. Gibson, H. Zhou. Dynamic estimation of volatility risk premia and investor risk aversion from option-implied and realized volatilities [J]. Journal of Econometrics, 2011, 160(1): 235-245.
    [17] A. Manela, A. Moreira. News Implied Volatility and Disaster Concerns [J]. Journal of Financial Economics , 2017, 123(1): 204-215.
    [18] J. Wang, W. Li. Do Garch models give poor out-of-sample forecasting volatility [J]. The Journal of Quantitative & Technical Economics, 2005, (6): 74-86.
    [19] H. Huang, W. Zhong. Evaluation on volatility forecasting performance of GARCH-type models [J]. Chinese Journal of Management Science, 2007, 15(6): 13-19. 
    [20] Y. Wei, N. Yu. Volatility forecasting model and SPA test of Chinese stock market [J]. Journal of Financial Research, 2007, (7): 138-150.
    [21] L. Zhou. Empirical study on volatility’s modeling and forecasting effect of China’s market [J]. Mathematics in Practice and Theory, 2009, 39(3): 25-34.
    [22] Z. Zheng, Y. Huang. Volatility forecast: GARCH model vs implied volatility [J]. The Journal of Quantitative & Technical Economics, 2010, (1): 140-150.
    [23] Y. Wei. Volatility forecasting models for CSI300 index futures [J]. Journal of Management Sciences in China, 2010, 13(2): 66-76.
    [24] R. Becker, A. Clements. Volatility and the role of order book structure [R]. Working Paper, University of Manchester, 2010.
    [25] C. C. Chan, W. M. Fong. Realized volatility and transactions [J]. Journal of Banking and Finance, 2006, 30(7): 2063-2085.
    [26] D. Berger, A. Chaboud, E. Hjalmarsson. What drives volatility persistence in the foreign exchange market? [J] Journal of Financial Economics, 2009, 94(2): 192-213.
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