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Range Volatility: A Review of Models and Empirical Studies

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Handbook of Financial Econometrics and Statistics

Abstract

The literature on range volatility modeling has been rapidly expanding due to its importance and applications. This chapter provides alternative price range estimators and discusses their empirical properties and limitations. Besides, we review some relevant financial applications for range volatility, such as value-at-risk estimation, hedge, spillover effect, portfolio management, and microstructure issues.

In this chapter, we survey the significant development of range-based volatility models, beginning with the simple random walk model up to the conditional autoregressive range (CARR) model. For the extension to range-based multivariate volatilities, some approaches developed recently are adopted, such as the dynamic conditional correlation (DCC) model, the double smooth transition conditional correlation (DSTCC) GARCH model, and the copula method. At last, we introduce different approaches to build bias-adjusted realized range to obtain a more efficient estimator.

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Notes

  1. 1.

    See Garman and Klass (1980), Beckers(1983), Ball and Torous (1984), Wiggins (1991), Rogers and Satchell (1991), Kunitomo (1992), Yang and Zhang (2000), Alizadeh et al. (2002), Brandt and Diebold (2006), Brandt and Jones (2006), Chou (2005, 2006), Cheung (2007), Martens and van Dijk (2007), Chou and Wang (2007), Floros (2009), Chou et al. (2009), and Chou and Liu (2010, 2011).

  2. 2.

    Please refer to Engle and Russell (1998), Engle and Gallo (2006), and Manganelli (2005).

  3. 3.

    For asset i, z * i,t = r i,t /λ * i,t , where λ * i,t = adj i × λ i,t and \( ad{j}_i=\frac{{\overline{\sigma}}_i}{\overline{{\widehat{\lambda}}_i}} \). The scaled expected range λ * i,t is computed by a product of λ i,t and the adjusted coefficient adj i which is the ratio of the unconditional standard deviations \( {\overline{\sigma}}_i \) for the return series to the sample mean \( \overline{{\widehat{\lambda}}_i} \) of the estimated conditional range.

  4. 4.

    Silvennoien and Terasvirta (2008, 2009) proposed the smooth transition conditional correlation GARCH (STCC-GARCH) model and the double smooth transition conditional correlation GARCH (DSTCC-GARCH) model.

  5. 5.

    In some studies, range was used as one of the estimators to improve the explanatory power of models.

  6. 6.

    In general, it mainly comes from bid-ask bounce and varies with the sampling frequency.

  7. 7.

    For low-frequency data, Alizadeh et al. (2002) showed that the range estimator is efficient and free of microstructure noise.

  8. 8.

    The Samuelson (time-to-delivery) effect means that volatility increases when a futures contract approaches its delivery date. Ripple and Moosa (2009) also used the realized range to test the effect of maturity, trading volume, and open interest on crude oil futures. In contrast, Karali and Thurman (2010) just used the daily range to prove the Samuelson effect.

References

  • Akay, O., Griffiths, M. D., & Winters, D. B. (2010). On the robustness of range-based volatility estimators. Journal of Financial Research, 33, 179–199.

    Article  Google Scholar 

  • Alizadeh, S., Brandt, M., & Diebold, F. (2002). Range-based estimation of stochastic volatility models. Journal of Finance, 57, 1047–1091.

    Article  Google Scholar 

  • Andersen, T., Bollerslev, T., Diebold, F., & Ebens, H. (2001). The distribution of realized stock return volatility. Journal of Financial Economics, 61, 43–76.

    Article  Google Scholar 

  • Andersen, T., Bollerslev, T., Diebold, F., & Labys, P. (2003). Modeling and forecasting realized volatility. Econometrica, 71, 579–625.

    Article  Google Scholar 

  • Andersen, T., Bollerslev, T., Christoffersen, P., & Diebold, F. (2006). Volatility and correlation forecasting. In G. C. Elliott, W. J. Granger, & A. Timmermann (Eds.), Handbook of economic forecasting (pp. 778–878). Amsterdam: North-Holland.

    Google Scholar 

  • Andersen, T., Bollerslev, T., Christoffersen, P., & Diebold, F. (2007). Practical volatility and correlation modeling for financial market risk management. In M. Carey & R. Stulz (Eds.), The risks of financial institutions (pp. 513–548). Chicago: University of Chicago Press for NBER.

    Chapter  Google Scholar 

  • Asai, M., & Brugal, I. (2012). Forecasting volatility using range data: Analysis for emerging equity markets in Latin America. Applied Financial Economics, 22, 461–470.

    Article  Google Scholar 

  • Asai, M., & Unite, A. (2010). General asymmetric stochastic volatility models using range data: Estimation and empirical evidence from emerging equity markets. Applied Financial Economics, 20, 1041–1049.

    Article  Google Scholar 

  • Ball, C., & Torous, W. (1984). The maximum likelihood estimation of security price volatility: Theory, evidence, and application to option pricing. Journal of Business, 57, 97–112.

    Article  Google Scholar 

  • Bannouh, K., van Dijk, D., & Martens, M. (2009). Range-based covariance estimation using high-frequency data: The realized co-range. Journal of Financial Econometrics, 7, 341–372.

    Article  Google Scholar 

  • Barndorff-Nielsen, O. E., & Shephard, N. (2005). How accurate is the asymptotic approximation to the distribution of realized variance. Identification and inference for econometric models. A Festschrift in honour of TJ Rothenberg, 306–311.

    Google Scholar 

  • Bauwens, L., Laurent, S., & Rombouts, J. V. K. (2006). Multivariate GARCH models: A survey. Journal of Applied Econometrics, 21, 79–109.

    Article  Google Scholar 

  • Beckers, S. (1983). Variances of security price returns based on highest, lowest, and closing prices. Journal of Business, 56, 97–112.

    Article  Google Scholar 

  • Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31, 307–327.

    Article  Google Scholar 

  • Bollerslev, T. (1990). Modeling the coherence in short-run nominal exchange rates: A multivariate generalized ARCH model. Review of Economics and Statistics, 72, 498–505.

    Article  Google Scholar 

  • Bollerslev, T., Chou, R. Y., & Kroner, K. (1992). ARCH modeling in finance: A review of the theory and empirical evidence. Journal of Econometrics, 52, 5–59.

    Article  Google Scholar 

  • Brandt, M., & Diebold, F. (2006). A no-arbitrage approach to range-based estimation of return covariances and correlations. Journal of Business, 79, 61–74.

    Article  Google Scholar 

  • Brandt, M., & Jones, C. (2006). Volatility forecasting with range-based EGARCH models. Journal of Business and Economic Statistics, 24, 470–486.

    Article  Google Scholar 

  • Brownlees, C. T., & Gallo, G. M. (2010). Comparison of volatility measures: A risk management perspective. Journal of Financial Econometrics, 8, 29–56.

    Article  Google Scholar 

  • Cai, Y., Chou, R. Y., & Li, D. (2009). Explaining international stock correlations with CPI fluctuations and market volatility. Journal of Banking and Finance, 33, 2026–2035.

    Article  Google Scholar 

  • Cappiello, L., Engle, R., & Sheppard, K. (2006). Asymmetric dynamics in the correlations of global equity and bond returns. Journal of Financial Econometrics, 4, 537–572.

    Article  Google Scholar 

  • Chen, C., & Wu, C. (2009). Small trades and volatility increases after stock splits. International Review of Economics and Finance, 18, 592–610.

    Article  Google Scholar 

  • Chen, C. W. S., Gerlach, R., & Lin, E. M. H. (2008). Volatility forecasting using threshold heteroskedastic models of the intra-day range. Computational Statistics and Data Analysis, 52, 2990–3010.

    Article  Google Scholar 

  • Chen, C. W. S., Gerlach, R., Hwang, B. B. K., & McAleer, M. (2012). Forecasting value-at-risk using nonlinear regression quantiles and the intra-day range. International Journal of Forecasting, 28, 557–574.

    Article  Google Scholar 

  • Cheung, Y. (2007). An empirical model of daily highs and lows. International Journal of Finance and Economics, 12, 1–20.

    Article  Google Scholar 

  • Cheung, Y., Cheung, Y., & Wan, A. (2009). A high–low model of daily stock price ranges. Journal of Forecasting, 28, 103–119.

    Article  Google Scholar 

  • Chiang, M., & Wang, L. (2011). Volatility contagion: A range-based volatility approach. Journal of Econometrics, 165, 175–189.

    Article  Google Scholar 

  • Chou, R. (2005). Forecasting financial volatilities with extreme values: The conditional autoregressive range (CARR) model. Journal of Money, Credit, and Banking, 37, 561–582.

    Article  Google Scholar 

  • Chou, R. (2006). Modeling the asymmetry of stock movements using price ranges. Advances in Econometrics, 20A, 231–257.

    Article  Google Scholar 

  • Chou, R. Y., & Cai, Y. (2009). Range-based multivariate volatility model with double smooth transition in conditional correlation. Global Finance Journal, 20, 137–152.

    Article  Google Scholar 

  • Chou, R. Y., & Liu, N. (2010). The economic value of volatility timing using a range-based volatility model. Journal of Economic Dynamics and Control, 34, 2288–2301.

    Article  Google Scholar 

  • Chou, R. Y., & Liu, N. (2011). Estimating time-varying hedge ratios with a range-based multivariate volatility model, Working paper, Academia Sinica.

    Google Scholar 

  • Chou, H., & Wang, D. (2007). Forecasting volatility of UK stock market: A test of conditional autoregressive range (CARR) model. International Research Journal of Finance and Economics, 10, 7–13.

    Google Scholar 

  • Chou, R. Y., Wu, C., & Liu, N. (2009). Forecasting time-varying covariance with a range-based dynamic conditional correlation model. Review of Quantitative Finance and Accounting, 33, 327–345.

    Article  Google Scholar 

  • Chou, H., Zaabar, R., & Wang, D. (2103). Measuring and testing the long-term impact of terrorist attacks on the US futures market. Applied Economics, 45, 225–238.

    Article  Google Scholar 

  • Christensen, K., & Podolskij, M. (2007). Realized range-based estimation of integrated variance. Journal of Econometrics, 141, 323–349.

    Article  Google Scholar 

  • Christensen, K. M., Christensen, K., Podolskij, M., & Vetter, M. (2009). Bias-correcting the realized range-based variance in the presence of market microstructure noise. Finance and Stochastics, 13, 239–268.

    Article  Google Scholar 

  • Christoffersen, P. F. (2002). Elements of financial risk management. San Diego: Academic.

    Google Scholar 

  • Cipollini, F., Engle, R. F., & Gallo, G. M. (2009). A model for multivariate non-negative valued processes in financial econometrics, Working paper.

    Google Scholar 

  • Corrado, C., & Truong, C. (2007). Forecasting stock index volatility: Comparing implied volatility and the intraday high-low price range. Journal of Financial Research, 30, 201–215.

    Article  Google Scholar 

  • Cox, J., & Rubinstein, M. (1985). Options markets. Englewood Cliffs: Prentice-Hall.

    Google Scholar 

  • Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50, 987–1007.

    Article  Google Scholar 

  • Engle, R. (2002a). Dynamic conditional correlation: A simple class of multivariate GARCH models. Journal of Business and Economic Statistics, 20, 339–350.

    Article  Google Scholar 

  • Engle, R. (2002b). New frontiers for ARCH models. Journal of Applied Econometrics, 17, 425–446.

    Article  Google Scholar 

  • Engle, R., & Gallo, G. M. (2006). A multiple indicators model for volatility using intra-daily data. Journal of Econometrics, 131, 3–27.

    Article  Google Scholar 

  • Engle, R., & Russell, J. R. (1998). Autoregressive conditional duration: A new model for irregularly spaced transaction data. Econometrica, 66, 1127–1162.

    Article  Google Scholar 

  • Engle, R., & Sheppard, K. (2001). Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH, NBER Working paper 8554.

    Google Scholar 

  • Engle, R., Gallo, G. M., & Velucchi, M. (2012). Volatility spillovers in East Asian financial markets: A MEM-based approach. Review of Economics and Statistics, 94, 222–223.

    Article  Google Scholar 

  • Fernandes, M., Mota, B., & Rocha, G. (2005). A multivariate conditional autoregressive range model. Economics Letters, 86, 435–440.

    Article  Google Scholar 

  • Floros, C. (2009). Modelling volatility using high, low, open and closing prices: Evidence from four S&P indices. International Research Journal of Finance and Economics, 28, 198–206.

    Google Scholar 

  • Gallant, R., Hsu, C., & Tauchen, G. (1999). Using daily range data to calibrate volatility diffusions and extracting integrated volatility. Review of Economics and Statistics, 81, 617–631.

    Article  Google Scholar 

  • Gallo, G. M., & Otranto, E. (2008). Volatility spillovers, interdependence and comovements: A Markov switching approach. Computational Statistics and Data Analysis, 52, 3011–3026.

    Article  Google Scholar 

  • Garman, M., & Klass, M. (1980). On the estimation of security price volatilities from historical data. Journal of Business, 53, 67–78.

    Article  Google Scholar 

  • Grammatikos, T., & Saunders, A. (1986). Futures price variability: A test of maturity and volume effects. Journal of Business, 59, 319–330.

    Article  Google Scholar 

  • Hanke, J., & Wichern, D. (2005). Business forecasting (8th ed.). New York: Prentice Hall.

    Google Scholar 

  • Harris, R. D. F., & Yilmaz, F. (2010). Estimation of the conditional variance–covariance matrix of returns using the intraday range. International Journal of Forecasting, 26, 180–194.

    Article  Google Scholar 

  • Harris, R. D. F., Stoja, E., & Yilmaz, F. (2011). A cyclical model of exchange rate volatility. Journal of Banking and Finance, 35, 3055–3064.

    Article  Google Scholar 

  • Harvey, A., Ruiz, E., & Shephard, N. (1994). Multivariate stochastic variance models. Review of Economic Studies, 61, 247–264.

    Article  Google Scholar 

  • He, A., & Wan, A. (2009). Predicting daily highs and lows of exchange rates: A cointegration analysis. Journal of Applied Statistics, 36, 1191–1204.

    Article  Google Scholar 

  • He, A., Kwok, J., & Wan, A. (2010). An empirical model of daily highs and lows of West Texas intermediate crude oil prices. Energy Economics, 32, 1499–1506.

    Article  Google Scholar 

  • Hsieh, D. A. (1991). Chaos and nonlinear dynamics: Application to financial markets. Journal of Finance, 46, 1839–1877.

    Article  Google Scholar 

  • Hsieh, D. A. (1993). Implications of nonlinear dynamics for financial risk management. Journal of Financial and Quantitative Analysis, 28, 41–64.

    Article  Google Scholar 

  • Kalev, P. S., & Duong, H. N. (2008). A test of the Samuelson hypothesis using realized range. Journal of Futures Markets, 28, 680–696.

    Article  Google Scholar 

  • Karali, B., & Thurman, W. N. (2010). Components of grain futures price volatility. Journal of Agricultural and Resource Economics, 35, 167–182.

    Google Scholar 

  • Karanasos, M., & Kartsaklas, A. (2009). Dual long-memory, structural breaks and the link between turnover and the range-based volatility. Journal of Empirical Finance, 16, 838–851.

    Article  Google Scholar 

  • Kunitomo, N. (1992). Improving the Parkinson method of estimating security price volatilities. Journal of Business, 65, 295–302.

    Article  Google Scholar 

  • Lee, O., & Shin, D. W. (2008). Geometric ergodicity and β-mixing property for a multivariate CARR model. Economics Letters, 100, 111–114.

    Article  Google Scholar 

  • Li, H., & Hong, Y. (2011). Financial volatility forecasting with range-based autoregressive volatility model. Finance Research Letters, 8, 69–76.

    Article  Google Scholar 

  • Lin, J., & Rozeff, M. S. (1994). Variance, return, and high-low price spreads. Journal of Financial Research, 17, 301–319.

    Article  Google Scholar 

  • Lin, E. M. H., Chen, C. W. S., & Gerlach, R. (2012). Forecasting volatility with asymmetric smooth transition dynamic range models. International Journal of Forecasting, 28, 384–399.

    Article  Google Scholar 

  • Liu, H., & Hung, J. (2010). Forecasting volatility and capturing downside risk of the Taiwanese futures markets under the financial tsunami. Managerial Finance, 36, 860–875.

    Article  Google Scholar 

  • Liu, H., Chiang, S., & Cheng, N. (2012). Forecasting the volatility of S&P depositary receipts using GARCH-type models under intraday range-based and return-based proxy measures. International Review of Economics and Finance, 22, 78–91.

    Article  Google Scholar 

  • Louzis, D. P., Xanthopoulos-Sisinis, S., & Refenes, A. N. (2012). The role of high frequency intra-daily data, daily range and implied volatility in multi-period value-at-risk forecasting, Working paper.

    Google Scholar 

  • Mandelbrot, B. (1971). When can price be arbitraged efficiently? A limit to validity of the random walk and martingale models. Review of Economics and Statistics, 53, 225–236.

    Article  Google Scholar 

  • Manganelli, S. (2005). Duration, volume and volatility impact of trades. Journal of Financial Markets, 8, 377–399.

    Article  Google Scholar 

  • Martens, M., & van Dijk, D. (2007). Measuring volatility with the realized range. Journal of Econometrics, 138, 181–207.

    Article  Google Scholar 

  • McAleer, M., & Medeiros, M. (2008). Realized volatility: A review. Econometric Reviews, 27, 10–45.

    Article  Google Scholar 

  • Molnár, P. (2012). Properties of range-based volatility estimators. International Review of Financial Analysis, 23, 20–29.

    Article  Google Scholar 

  • Nelson, D. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59, 347–370.

    Article  Google Scholar 

  • Parkinson, M. (1980). The extreme value method for estimating the variance of the rate of return. Journal of Business, 53, 61–65.

    Article  Google Scholar 

  • Patton, A. J. (2011). Volatility forecast comparison using imperfect volatility proxies. Journal of Econometrics, 160, 246–256.

    Article  Google Scholar 

  • Poon, S. H., & Granger, C. W. J. (2003). Forecasting volatility in financial markets: A review. Journal of Economic Literature, 41, 478–639.

    Article  Google Scholar 

  • Ripple, R. D., & Moosa, I. A. (2009). The effect of maturity, trading volume, and open interest on crude oil futures price range-based volatility. Global Finance Journal, 20, 209–219.

    Article  Google Scholar 

  • Rogers, L., & Satchell, S. (1991). Estimating variance from high, low and closing prices. Annals of Applied Probability, 1, 504–512.

    Article  Google Scholar 

  • Rogers, L., & Zhou, F. (2008). Estimating correlation from high, low, opening and closing prices. The Annals of Applied Probability, 18, 813–823.

    Article  Google Scholar 

  • Rogers, L., Satchell, S., & Yoon, Y. (1994). Estimating the volatility of stock prices: A comparison of methods that use high and low prices. Applied Financial Economics, 4, 241–247.

    Article  Google Scholar 

  • Shao, X., Lian, Y., & Yin, L. (2009). Forecasting value-at-risk using high frequency data: The realized range model. Global Finance Journal, 20, 128–136.

    Article  Google Scholar 

  • Shu, J. H., & Zhang, J. E. (2006). Testing range estimators of historical volatility. Journal of Futures Markets, 26, 297–313.

    Article  Google Scholar 

  • Silvennoinen, A., & Teräsvirta, T. (2008). Multivariate autoregressive conditional heteroskedasticity with smooth transition in conditional correlations, SSE/EFI Working paper series in Economics and Finance.

    Google Scholar 

  • Silvennoinen, A., & Teräsvirta, T. (2009). Modeling multivariate autoregressive conditional heteroskedasticity with the double smooth transition conditional correlations GARCH model. Journal of Financial Econometrics, 7, 373–411.

    Article  Google Scholar 

  • Taylor, S. J. (1986). Modelling financial time series. Chichester: Wiley.

    Google Scholar 

  • Todorova, N. (2012). Volatility estimators based on daily price ranges versus the realized range. Applied Financial Economics, 22, 215–229.

    Article  Google Scholar 

  • Wiggins, J. (1991). Empirical tests of the bias and efficiency of the extreme-value variance estimator for common stocks. Journal of Business, 64, 417–432.

    Article  Google Scholar 

  • Wu, C., & Liang, S. (2011). The economic value of range-based covariance between stock and bond returns with dynamic copulas. Journal of Empirical Finance, 18, 711–727.

    Article  Google Scholar 

  • Yang, D., & Zhang, Q. (2000). Drift-independent volatility estimation based on high, low, open, and closing prices. Journal of Business, 73, 477–491.

    Article  Google Scholar 

  • Yeh, J.,Wang, J., & Kuan, C. (2009). A noise-robust estimator of volatility based on interquantile ranges, Working paper.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Economics, Academia Sinica and National Chiao Tung University, Taipei, Taiwan

    Ray Yeutien Chou

  2. Department of Shipping and Transportation Management, National Taiwan Ocean University, Keelung, Taiwan

    Hengchih Chou

  3. Department of Finance, Feng Chia University, Taichung, Taiwan

    Nathan Liu

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  1. Ray Yeutien Chou
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  2. Hengchih Chou
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  1. Department of Finance and Economics, Rutgers Business School, Rutgers, The State University of New Jersey, Piscataway, New Jersey, USA

    Cheng-Few Lee

  2. Center for PBBEF Research, North Brunswick, New Jersey, USA

    John C. Lee

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Chou, R.Y., Chou, H., Liu, N. (2015). Range Volatility: A Review of Models and Empirical Studies. In: Lee, CF., Lee, J. (eds) Handbook of Financial Econometrics and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7750-1_74

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