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A conditional autoregressive range model with gamma distribution for financial volatility modelling

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  • Xie, Haibin
  • Wu, Xinyu

Abstract

The commonly used conditional autoregressive range model with Weibull distribution (henceforth WCARR) suffers from serious inlier problem. We conjecture that this problem is due to a misspecified distribution to the disturbance, and propose a conditional autoregressive range model with gamma distribution (henceforth GCARR) to model the volatility of financial assets. In this paper, we first discuss the theoretical properties of the GCARR model and then compare its empirical performance with the WCARR. Empirical studies are performed on a broad set of stock indices in different countries over different time horizons. Consistent with the conjecture, we find that the GCARR model can reduce not only the inlier problem but also the outlier problem of the WCARR model. The results indicate that our GCARR model describes the dynamics of the range-based volatility better than the WCARR model and thus serves as a better benchmark.

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  • Xie, Haibin & Wu, Xinyu, 2017. "A conditional autoregressive range model with gamma distribution for financial volatility modelling," Economic Modelling, Elsevier, vol. 64(C), pages 349-356.
    • Handle: RePEc:eee:ecmode:v:64:y:2017:i:c:p:349-356
    DOI: 10.1016/j.econmod.2017.04.001
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    as
    1. Duan, Jin-Chuan, 1997. "Augmented GARCH (p,q) process and its diffusion limit," Journal of Econometrics, Elsevier, vol. 79(1), pages 97-127, July.
    2. Garman, Mark B & Klass, Michael J, 1980. "On the Estimation of Security Price Volatilities from Historical Data," The Journal of Business, University of Chicago Press, vol. 53(1), pages 67-78, January.
    3. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    4. Campbell, John & Shiller, Robert, 1988. "Stock Prices, Earnings, and Expected Dividends," Scholarly Articles 3224293, Harvard University Department of Economics.
    5. Miao, Daniel Wei-Chung & Wu, Chun-Chou & Su, Yi-Kai, 2013. "Regime-switching in volatility and correlation structure using range-based models with Markov-switching," Economic Modelling, Elsevier, vol. 31(C), pages 87-93.
    6. Chou, Ray Yeutien & Liu, Nathan, 2010. "The economic value of volatility timing using a range-based volatility model," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2288-2301, November.
    7. Martens, Martin & van Dijk, Dick, 2007. "Measuring volatility with the realized range," Journal of Econometrics, Elsevier, vol. 138(1), pages 181-207, May.
    8. Mandelbrot, Benoit B, 1971. "When Can Price Be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models," The Review of Economics and Statistics, MIT Press, vol. 53(3), pages 225-236, August.
    9. Anderson, Randy I. & Chen, Yi-Chi & Wang, Li-Min, 2015. "A range-based volatility approach to measuring volatility contagion in securitized real estate markets," Economic Modelling, Elsevier, vol. 45(C), pages 223-235.
    10. Wiggins, James B, 1991. "Empirical Tests of the Bias and Efficiency of the Extreme-Value Variance Estimator for Common Stocks," The Journal of Business, University of Chicago Press, vol. 64(3), pages 417-432, July.
    11. Robert Engle, 2002. "New frontiers for arch models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 425-446.
    12. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    13. Jeff Fleming & Chris Kirby & Barbara Ostdiek, 2001. "The Economic Value of Volatility Timing," Journal of Finance, American Finance Association, vol. 56(1), pages 329-352, February.
    14. Cuthbertson, Keith & Hyde, Stuart, 2002. "Excess volatility and efficiency in French and German stock markets," Economic Modelling, Elsevier, vol. 19(3), pages 399-418, May.
    15. Degiannakis, Stavros & Livada, Alexandra, 2013. "Realized volatility or price range: Evidence from a discrete simulation of the continuous time diffusion process," Economic Modelling, Elsevier, vol. 30(C), pages 212-216.
    16. Giovanni Barone Adesi & Robert F. Engle & Loriano Mancini, 2014. "A GARCH Option Pricing Model with Filtered Historical Simulation," Palgrave Macmillan Books, in: Giovanni Barone Adesi (ed.), Simulating Security Returns: A Filtered Historical Simulation Approach, chapter 4, pages 66-108, Palgrave Macmillan.
    17. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    18. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January.
    19. repec:bla:jfinan:v:43:y:1988:i:3:p:661-76 is not listed on IDEAS
    20. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    21. Brandt, Michael W. & Jones, Christopher S., 2006. "Volatility Forecasting With Range-Based EGARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 470-486, October.
    22. Yang, Dennis & Zhang, Qiang, 2000. "Drift-Independent Volatility Estimation Based on High, Low, Open, and Close Prices," The Journal of Business, University of Chicago Press, vol. 73(3), pages 477-491, July.
    23. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range‐Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1047-1091, June.
    24. Liu, Jing & Wei, Yu & Ma, Feng & Wahab, M.I.M., 2017. "Forecasting the realized range-based volatility using dynamic model averaging approach," Economic Modelling, Elsevier, vol. 61(C), pages 12-26.
    25. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
    26. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    27. Chou, Ray Yeutien, 2005. "Forecasting Financial Volatilities with Extreme Values: The Conditional Autoregressive Range (CARR) Model," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(3), pages 561-582, June.
    28. Christensen, Kim & Podolskij, Mark, 2007. "Realized range-based estimation of integrated variance," Journal of Econometrics, Elsevier, vol. 141(2), pages 323-349, December.
    29. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

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    3. Tan, Shay-Kee & Ng, Kok-Haur & Chan, Jennifer So-Kuen & Mohamed, Ibrahim, 2019. "Quantile range-based volatility measure for modelling and forecasting volatility using high frequency data," The North American Journal of Economics and Finance, Elsevier, vol. 47(C), pages 537-551.
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    6. Wu, Xinyu & Xie, Haibin & Zhang, Huanming, 2022. "Time-varying risk aversion and renminbi exchange rate volatility: Evidence from CARR-MIDAS model," The North American Journal of Economics and Finance, Elsevier, vol. 61(C).

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