Volatility plays a central role in many areas of finance. In view of the theoretical and practical studies, the price range provides an intuitive and efficient estimator of volatility. In this paper, we propose a new range model, which incorporates the superiority of range in forecasting volatility and of range and the elasticity of the DCC model. It contributes to the multivariate applications and can be led into broad applications in finance.
This dissertation provides three empirical methods to strengthen the suitability of the new range-based volatility model. To begin with a statistical test, the range-based DCC model performs better than other selected models for the four covariance benchmarks. Then, we test its economic value and compare its performance with the return-based DCC model. We conclude that the range-based DCC model obtains higher economic value than the return-based one. Finally, we apply the range model to calculate hedge ratios. Based on minimum-variance hedge criterion, range-based volatility models have better performance in most commodities.
Undoubtedly, the range is sensitive to outliers in statistics, and however only few researches mention this problem. It’s useful and meaningful to utilize the quantile range to replace the standard range to get a robust measure of range. Moreover, the multivariate works for range are still in its infancy. Future research is obviously required for this topic.
Reference
Alizadeh, S., M. Brandt, and F. Diebold (2002), Range-based estimation of stochastic volatility models, Journal of Finance, 57, 1047-91.
Andersen, T., T. Bollerslev, F. Diebold, and H. Ebens (2001), The distribution of realized stock return volatility, Journal of Financial Economics, 61, 43-76.
Baillie, R. T., and R. J. Myers (1991). Bivariate GARCH estimation of the optimal commodity futures hedge, Journal of Applied Econometrics, 6, 109-124.
Bollerslev, T. (1986) Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31, 307-328.
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.
Bollerslev, T., R. Y. Chou, and K. Kroner (1992), ARCH modeling in finance: A review of the theory and empirical evidence, Journal of Econometrics, 52, 5-59.
Bollerslev, T., R.F. Engle, and J. M. Wooldridge (1988), A capital asset pricing model with time varying covariances, Journal of Political Economy, 96, 116-31.
Bollerslev, T., R.F. Engle, and D. Nelson (1994), ARCH Models, in Handbook of Econometrics, IV, 2959-3038, ed. Engle, R.F., and McFadden, D.C., Amsterdam:
North-Holland.
Brandt, M. and C. Jones (2006), Volatility forecasting with range-based EGARCH models, Journal of Business and Economic Statistics, 24, 470-86.
Busse, J.A. (1999), Volatility timing in mutual funds: Evidence from daily returns, Review of Financial Studies, 12, 1009-1041.
Cappiello, L., R.F. Engle, and K. Sheppard (2006), Asymmetric dynamics in the correlations of global equity and bond returns, Journal of Financial Econometrics 4, 537-72.
Chen, S. S., C.F. Lee, and K. Shrestha (2001), Futures hedge ratios: A review.
Quarterly Review of Economics and Finance, 43, 433-465.
Chou, R. Y. (2005), Forecasting financial volatilities with extreme values: The
conditional autoregressive range (CARR) model, Journal of Money Credit and Banking, 37, 561-82.
Chou, R. Y. (2006), Modeling the asymmetry of stock movements using price ranges, Advances in Econometrics, 20, 231-58.
Chou, R.Y., C.C. Wu, and N. Liu (2007), Forecasting time-varying Covariance with a range-based dynamic conditional correlation model, Working Paper (Academia Sinica).
Connolly, R., C. Stivers, and L. Sun (2005), Stock market uncertainty and the stock-bond return relation, Journal of Financial and Quantitative Analysis, 40, 161-194.
Cox, J. and M. Rubinstein (1985), Options markets, Prentice-Hall, NJ.
Edrington, L. H. (1979), The hedging performance of the new futures markets, Journal of Finance, 34, 157-170.
Engle, R.F. (2002a), Dynamic conditional correlation: A simple class of multivariate GARCH models, Journal of Business and Economic Statistics, 20, 339-50.
Engle, R.F. (2002b), New frontiers for ARCH models, Journal of Applied Econometrics, 17, 425- 446.
Engle, R.F. (2004), Risk and volatility: Econometric models and financial practice, American Economic Review, 94, 405-20.
Engle, R.F. and R. Colacito (2006). Testing and valuing dynamic correlations for asset allocation, Journal of Business and Economic Statistics, 24, 238-253.
Engle, R.F. and K. Kroner (1995), Multivariate simultaneous GARCH, Econometric Theory, 11, 122-50.
Engle, R.F. and S. Manganelli (2004), CAViaR: Conditional autoregressive Value at Risk by regression quantiles, Journal of Business and Economic Statistics, 22, 367-81.
Engle, R.F. and K. Sheppard (2001), Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH, Working Paper (University of California, San Diego).
Engle, R.F. and J. Russell (1998), Autoregressive conditional duration: A new model
for irregular spaced transaction data, Econometrica, 66, 1127-1162.
Fama, E. F. (1965), The behavior of stock market prices, Journal of Business, 38, 34-105.
Ferland, R. and S. Lalancette (2006), Dynamics of realized volatilities and correlations: An empirical study, Journal of Banking and Finance, 30, 2109-2130.
Fernades, M., B. Mota, and G. Rocha (2005), A multivariate conditional autoregressive range model, Economics Letters, 86, 435-440.
Fleming, J., C. Kirby, and B. Ostdiek (2001), The economic value of volatility timing.
Journal of Finance, 56, 329-352.
Fleming, J., C. Kirby, and B. Ostdiek (2003), The economic value of volatility timing using realized volatility, Journal of Financial Economics, 67, 473-509.
Foster, D.P. and D.B. Nelson (1996), Continuous record asymptotics for rolling sample variance estimators, Econometrica, 64, 139-174.
French, K. R., G. W. Schwert, and R. F. Stambaugh (1987), Expected stock returns and volatility, Journal of Financial Economics, 19, 3-29.
Gallant, R., C. Hsu, and G. Tauchen (1999), Using daily range data to calibrate volatility diffusions and extracting integrated volatility, Review of Economics and Statistics, 81, 617-31.
Garman, M., and M. Klass (1980), On the estimation of security price volatilities from historical data, Journal of Business, 53, 67-78.
Hafner, C. M. and P. H. Franses (2003), A generalized dynamic conditional correlation model for many asset returns, Working Paper (Erasmus University Rotterdam).
Johnson, L. L. (1960), The theory of hedging and speculation in commodity futures.
Reviews of Economic Studies, 27, 139-151.
Kroner K. F. and J. Sultan (1993), Time-varying distributions and dynamic hedging with foreign currency futures, Journal of Finance and Quantitative analysis, 28,
535-551.
Kunitomo, N. (1992), Improving the Parkinson method of estimating security price volatilities, Journal of Business, 65, 295-302.
Lence, S. H. (1995), The economic value of minimum-variance hedges. American Journal of Agricultural Economics, 77, 353–364.
Lien, D and Y.K. Tse (2002), Some recent developments in futures hedging, Journal of Economic Surveys, 16, 357-396.
Lien, D., Y.K. Tse, and A. Tsui (2002), Evaluating the hedging performance of the constant-correlation GARCH model, Applied Financial Econometrics, 12, 791-798.
Lien, D. and L. Yang (2006), Spot-futures spread, time-varying, and hedging with currency futures, Journal of Futures Markets, 26, 1019-1038.
Mandelbrot, B. (1963), The variation of certain speculative prices, Journal of Business, 36, 394-419.
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.
Marquering, W. and M. Verbeek (2004), The economic value of predicting stock index returns and volatility, Journal of Financial and Quantitative Analysis, 39, 407-429.
Martens, M. and D. van Dijk (2007), Measuring volatility with the realized range’, Journal of Econometrics, 138, 181-207.
Merton, R.C. (1980), On estimating the expected return on the market: An exploratory investigation, Journal of Financial Economics, 8, 323-361.
Newey, W. and K. West (1987), A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix, Econometrica, 55, 703-8.
Nison, S. (1991), Japanese candlestick charting techniques, New York Institute of Finance, New York.
Parkinson, M. (1980), The extreme value method for estimating the variance of the rate of return, Journal of Business, 53, 61-5.
Rogers, L. C. G. and S. E. Satchell (1991), Estimating variance from high, low and closing prices, Annals of Applied Probability, 1, 504-12.
Shu, J.H. and J.E Zhang (2006), Testing range estimators of historical volatility,
Journal of Futures Markets, 26, 297-313.
Stein, J. L. (1961), The simultaneous determination of spot and futures prices, American Economic Review, 51, 1012-1025.
Taylor, N. (2004), Trading intensity, volatility, and arbitrage activity, Journal of Banking and Finance, 28, 1137-62.
Thorp, S. and G. Milunovich (2007), Symmetric versus asymmetric conditional covariance forecasts: Does it pay to switch. Journal of Financial Research, 30, 355-377.
Tsay, R. S. (2002), Analysis of financial time series (John Wiley publications, New York).
Tse, Y. K. and A. K. C. Tsui (2002), A multivariate GARCH model with time-varying correlations, Journal of Business and Economic Statistics, 20, 351-62.
West, K.D., H.J. Edison, and D. Cho (1993), A utility-based comparison of some models of exchange rate volatility, Journal of International Economics, 35, 23-45.
White, H. (1994), Estimation, Inference, and Specification Analysis (Cambridge University Press).
Wiggins, J. (1991), Empirical tests of the bias and efficiency of the extreme-value variance estimator for common stocks, Journal of Business, 64, 417-32.
Yang, D. and Q. Zhang (2000), Drift independent volatility estimation based on high, low, open, and close prices, Journal of Business, 73, 477-91.