The role of high frequency intra-daily data, daily range and implied volatility in multi-period Value-at-Risk forecasting

Louzis, Dimitrios P. and Xanthopoulos-Sisinis, Spyros and Refenes, Apostolos P. (2011): The role of high frequency intra-daily data, daily range and implied volatility in multi-period Value-at-Risk forecasting.

Abstract

In this paper, we assess the informational content of daily range, realized variance, realized bipower variation, two time scale realized variance, realized range and implied volatility in daily, weekly, biweekly and monthly out-of-sample Value-at-Risk (VaR) predictions. We use the recently proposed Realized GARCH model combined with the skewed student distribution for the innovations process and a Monte Carlo simulation approach in order to produce the multi-period VaR estimates. The VaR forecasts are evaluated in terms of statistical and regulatory accuracy as well as capital efficiency. Our empirical findings, based on the S&P 500 stock index, indicate that almost all realized and implied volatility measures can produce statistically and regulatory precise VaR forecasts across forecasting horizons, with the implied volatility being especially accurate in monthly VaR forecasts. The daily range produces inferior forecasting results in terms of regulatory accuracy and Basel II compliance. However, robust realized volatility measures such as the adjusted realized range and the realized bipower variation, which are immune against microstructure noise bias and price jumps respectively, generate superior VaR estimates in terms of capital efficiency, as they minimize the opportunity cost of capital and the Basel II regulatory capital. Our results highlight the importance of robust high frequency intra-daily data based volatility estimators in a multi-step VaR forecasting context as they balance between statistical or regulatory accuracy and capital efficiency.

• Item Type: MPRA Paper
• Language: English
• Keywords: Realized GARCH; Value-at-Risk; multiple forecasting horizons; alternative volatility measures; microstructure noise; price jumps
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods

References

Alexander C. 2008a. Market Risk Analysis: Pricing, Hedging and Trading Financial Instruments, vol III. Wiley: New York.

Alexander C. 2008b. Market Risk Analysis: Value-at-Risk Models, vol IV. Wiley: New York.

Alizadeh S, Brandt M, Diebold F. 2002. Range-based estimation of stochastic volatility models. Journal of Finance 57: 1047-1091.

Andersen TG, Bollerslev T. 1998. Answering the skeptics: Yes, standard volatility models do provide accurate forecasts. International Economic Review 39: 885-905.

Andersen TG, Bollerslev T, Diebold FX, Ebens H. 2001a. The distribution of realized stock returns volatility. Journal of Financial Economics 6: 43-76.

Andersen TG, Bollerslev T, Diebold FX, Labys P. 2001b. The distribution of realized exchange rate volatility. Journal of the American Statistical Association 96: 42-55.

Andersen TG, Bollerslev T, Diebold FX, Labys P. 2003. Modeling and forecasting realized volatility. Econometrica 71: 579-625.

Andersen TG, Bollerslev T, Christoffersen PF, Diebold FX. 2006. Volatility and correlation forecasting. In: Elliott, G., et al. (Eds.), Handbook of Economic Forecasting: Vol. I, North-Holland.

Angelidis T, Degiannakis S. 2008. Volatility forecasting: Intra-day versus Inter-day models. Journal of International Financial Markets, Institutions and Money 18: 449-465.

Angelidis T, Benos A, Degiannakis S. 2004. The use of GARCH models in VaR estimation. Statisitcal Methodology 1: 105-128.

Barndorff-Nielsen OE, Shephard N. 2002. Econometric analysis of realized volatility and its use in estimating stochastic volatility models. Journal of the Royal Statistical Society. B 64: 253-280.

Barndorff-Nielsen OE, Shephard N. 2004. Power and bipower variation with stochastic volatility and jumps. Journal of Financial Econometrics 2: 1-48.

Barndorff-Nielsen OE, Hansen PR, Lunde A,. Shephard N. 2008. Designing realized kernels to measure the ex post variation of equity prices in the presence of noise. Econometrica 76: 1481-1536.

Basel Committee on Banking Supervision. 1996a. Amendment to the Capital Accord to incorporate market risks. Bank for International Settlements: Basel.

Basle Committee on Banking Supervision 1996b. Supervisory framework for the use of backtesting in conjunction with the internal models approach to market risk capital requirements. Bank for International Settlements, Publication No. 22.

Basel Committee on Banking Supervision. 2006. International convergence of capital measurement and capital standards. Bank for International Settlements: Basel.

Becker R, Clements AE, McClelland A. 2009. The jump component of S&P 500 volatility and the VIX index. Journal of Banking and Finance 33: 1033-1038.

Beltratti A., Morana C. 2005. Statistical Benefits of Value-at-risk with long memory. Journal of Risk 7: 21-45.

Blair BJ, Poon S, Taylor SJ. 2001. Forecasting S&P 100 volatility: The incremental information content of implied volatility and high frequency index returns. Journal of Econometrics 105: 5-26.

Bollerslev T. 1986. Generalized autoregressive heteroskedasticity. Journal of Econometrics 31: 307-327.

Bollerslev T. 2010. Glossary to ARCH (GARCH). In: Bollerslev, T., et al. (Eds.), Volatility and time series econometrics: Essays in honor of Robert F. Engle. Oxford University Press.

Brandt MW, Diebold FX. 2003. A vp-arbitrage approach to range-based estimation of return covariances and correlations. NBER Working Paper No. 9664.

Brooks C, Persand G. 2003. Volatility forecasting for risk management. Journal of forecasting 22: 1-22.

Brownless CT, Gallo GM. 2010. Comparison of volatility measures: A risk management perspective. Journal of Financial Econometrics 8: 29-56.

Campel A., Chen XL. 2008. The year of living riskily. Risk July 2008: 28-32.

Chicago Board of Options Exchange. 2003. White Paper, VIX CBOE Volatility Index. Accessible from: http://www.cboe.com/micro/vix/introduction.aspx.

Christensen PJ, Prabhala NR. 1998. The relation of between implied and realized volatility. Journal of Financial Economics 50: 125-150.

Christensen K, Podolskij M. 2007. Realized range-based estimation of integrated variance. Journal of Econometrics 141: 323-349.

Christoffersen P. 1998. Evaluating interval forecasts. International Economic Review 39: 841-862.

Christoffersen PF. 2003. Elements of Financial Risk Management. Academic Press: San Diego.

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

Chou RY, Chou H, Liu N. 2010. Range volatility models and their applications in finance. ). In: Lee C-F, et al. (Eds.), Handbook of Quantitative Finance and Risk Management. Springer.

Corrado C, Miller TW. 2005. The forecast quality of CBOE implied volatility indexes. Journal of Futures Markets 25: 339-373.

Corrado C, Truong C. 2007. Forecasting stock index volatility: Comparing implied volatility and the intraday high-low price range. The Journal of Financial Research XXX: 201-207.

Diebold FX, Gunther TA, Tay AS. 1998. Evaluating density forecasts. International Economic Review 39: 863-883.

Drakos AA, Kouretas GP, Zarangas LP. 2010. Forecasting financial volatility of the Athens stock exchange daily returns: An application of the asymmetric normal mixture GARCH model. International Journal of Finance and Economics 15: 331-350.

Engle RF. 1982. Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50: 987-1007.

Engle RF. 2002. New frontiers for ARCH models. Journal of Applied Econometrics 17: 425-446.

Engle RF, Gallo JP. 2006. A multiple indicator model for volatility using intra daily data. Journal of Econometrics 131: 3-27.

Fernandez C, Steel M. 1998. On Bayesian modeling of fat tails and skeweness. Journal of the American Statistical Association 93: 359-371.

Ferreira MA., Lopez JA. 2005. Evaluating interest rate covariance models within a Value-at-Risk framework. Journal of Financial Econometrics 3: 126-168.

Forsberg L, Ghysels E. 2007. Why do absolute returns predict volatility so well? Journal of Financial Econometrics 5: 31-67.

Fuertes AM, Izzeldin M, Kalotychou E. 2009. On forecasting daily stock volatility: The role of intraday information and market conditions. International Journal of Forecasting 25: 259-281.

Garman M, Klass M. 1980. On the estimation of security price volatilities from historical data. Journal of Business 53: 67-78.

Ghysels E, Sinko A.. 2006. Comment on Hansen and Lunde JBES paper. Journal of Business and Economic Forecasting 26:192-194.

Ghysels E, Santa-Clara P, Valkanov R. 2006. Predicting volatility: How to get most out of returns data sampled at different frequencies. Journal of Econometrics 131: 59-95. Giot P, Laurent S. 2003a. Value-at-risk for long and short trading positions. Journal of Applied Econometrics 6: 641-663.

Giot P, Laurent S. 2003b. Market risk in commodity markets: A VaR approach. Energy Economics 25: 435-457.

Giot P, Laurent S. 2004. Modeling daily value-at-risk using realized volatility and ARCH type models. Journal of Empirical Finance 11: 379-398.

Giot P, Laurent S. 2007. The information content of implied volatility in the light of jump/continuous decomposition of realized volatility. The Journal of Future Markets 27: 337-359.

Giot P. 2005. Implied volatility indexes and daily Value at Risk models. The Journal of derivatives 12: 54-64.

Hamilton JD. 1994. Time Series Analysis. Princeton University Press: Princeton.

Hansen PR. 2005. A test for superior predictive ability. Journal of Business and Economic Statistics 23: 365-380.

Hansen PR, Huang Z, Shek HH. 2011. Realized GARCH: a joint model for returns and realized measures of volatility. Journal of Applied Econometrics. doi: 10.1002/jae.1234.

Koopman SJ, Jungbacker B, Hol E. 2005. Forecasting daily variability of the S&P100 stock index using historical, realised and implied volatility measurements. Journal of Empirical Finance 12: 445-475.

Kuester K, Mittnik S, Paolella MS. 2006. Value-at-Risk prediction: A comparison of alternative strategies. Journal of Financial Econometrics 4: 53-89.

Lambert P, Laurent S. 2001. Modelling financial time series using GARCH-type models and skewed Student density. Mimeo, Universite de Liege.

Lawerence CT, Tits AL. 2001. A computationally efficient feasible sequential quadratic programming algorithm. SIAM Journal on Optimization 11:1092-1118.

Li H, Hong H. 2011. Financial volatility forecasting with range-based autoregressive volatility model. Financial Research Letters 8: 69-76.

Liu C, Maheu JM. 2009. Forecasting realized volatility: A Bayesian model-averaging approach. Journal of Applied Econometrics 24: 709-733.

Lopez JA. 1999. Methods for evaluating Value-at-Risk estimates. Federal Reserve Bank of San Francisco Economic Review 2: 3-17.

Louzis DP, Xanthopoulos-Sisinis S, Refenes AP. 2011. Are realized volatility models good candidates for alternative Value-at-Risk prediction strategies? MPRA Working Paper.

Louzis DP, Xanthopoulos-Sisinis S, Refenes AP. 2012. Stock index realized volatility forecasting in the presence of heterogeneous leverage effects and long range dependence in the volatility of realized volatility. Applied Economics 44: 3533-3550.

Martens M. 2002. Measuring and forecasting S&P 500 index-futures volatility using high-frequency data. Journal of Futures Markets 22: 497-518.

Martens M, van Dijk D. 2007. Measuring volatility with realized range. Journal of Econometrics 138: 181-207.

Martens M, van Dijk D, Pooter M. 2009. Forecasting S&P 500 volatility: Long memory, level shifts, leverage effects, day of the week seasonality and macroeconomic announcements. International Journal of Forecasting 25: 282-303.

Parkison M. 1980. The extreme value method for estimating the variance of the rate of return. Journal of Business. 53: 61-65.

Poon S, Granger C. 2003. Forecasting volatility in financial markets: A review. Journal of Economic Literature 41: 478-539.

Rogers L, Satchell S. 1991. Estimating variance from high, low and closing prices. Annals of Applied Probability 1: 504-512.

Sajjad R, Coakley J, Nankervis JC. 2008. Markov-Switching GARCH modeling of Value-at-Risk. Studies in Nonlinear dynamics and Econometrics 12: Article 7.

Sarma M, Thomas S, Shah A. 2003. Selection of Value-at-Risk models. Journal of Forecasting 22: 337-358.

Shao XD, Lian YJ, Yin LQ, 2009. Forecasting Value-at-Risk using high frequency data: The realized range model. Global Finance Journal 20, 128-136.

Shu JH, Zhang JE. 2006. Testing range estimators of historical volatility. Journal of Future Markets 26: 297-313.

Watanabe T. 2011. Quintile forecasts of financial returns using Realized GARCH models. Hi-Stat Discussion Paper, Hitotsubashi University.

Zhang L, Mykland PA, Aït-Sahalia Y. 2005. A tale of two time scales: Determining integrated volatility with noisy high-frequency data. Journal of the American Statistical Association 100: 1394-1411.