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Modelling and Forecasting Unbiased Extreme Value Volatility Estimator: A Study Based on EUR/USD Exchange Rate

DOI: 10.4236/tel.2018.89102, PP. 1599-1613

Keywords: Volatility Modeling, Volatility Forecasting, Forecast Evaluation, Economic Significance Analysis, Bias-Corrected Extreme Value Estimator

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Abstract:

The paper provides a framework to model and forecast volatility of EUR/USD exchange rate based on the unbiased AddRS estimator as proposed by Kumar and Maheswaran [1]. The framework is based on the heterogeneous auto-regressive (HAR) model to capture the heterogeneity in a market and to ac-count for long memory in data. The results indicate that the framework based on the unbiased extreme value volatility estimator generates more accurate forecasts of daily volatility in comparison to alternative volatility models.

References

[1]  Kumar, D. and Maheswaran, S. (2014) A Reflection Principle for a Random Walk with Implications for Volatility Estimation Using Extreme Values of Asset Prices. Economic Modelling, 38, 33-44.
https://doi.org/10.1016/j.econmod.2013.11.045
[2]  Alizadeh, S., Brandt, M.W. and Diebold, F.X. (2002) Range-Based Estimation of Stochastic Volatility Models. The Journal of Finance, 57, 1047-1091.
https://doi.org/10.1111/1540-6261.00454
[3]  Rogers, L.C. and Zhou, F. (2008) Estimating Correlation from High, Low, Opening and Closing Prices. The Annals of Applied Probability, 18, 813-823.
https://doi.org/10.1214/07-AAP460
[4]  Parkinson, M. (1980) The Extreme Value Method for Estimating the Variance of the Rate of Return. Journal of Business, 53, 61-65.
https://doi.org/10.1086/296071
[5]  Garman, M.B. and Klass, M.J. (1980) On the Estimation of Security Price Volatilities from Historical Data. The Journal of Business, 53, 67-78.
https://doi.org/10.1086/296072
[6]  Rogers, L.C. and Satchell, S.E. (1991) Estimating Variance from High, Low and Closing Prices. The Annals of Applied Probability, 1, 504-512.
https://doi.org/10.1214/aoap/1177005835
[7]  Kunitomo, N. (1992) Improving the Parkinson Method of Estimating Security Price Volatilities. The Journal of Business, 65, 295-302.
https://doi.org/10.1086/296570
[8]  Yang, D. and Zhang, Q. (2000) Drift-Independent Volatility Estimation Based on High, Low, Open, and Close Prices. The Journal of Business, 73, 477-492.
https://doi.org/10.1086/209650
[9]  Ball, C.A. and Torous, W.N. (1984) The Maximum Likelihood Estimation of Security Price Volatility: Theory, Evidence, and Application to Option Pricing. The Journal of Business, 57, 97-112.
https://doi.org/10.1086/296226
[10]  Magdon-Ismail, M. and Atiya, A.F. (2003) A Maximum Likelihood Approach to Volatility Estimation for a Brownian Motion Using High, Low and Close Price Data. Quantitative Finance, 3, 376-384.
https://doi.org/10.1088/1469-7688/3/5/304
[11]  Horst, E.T., et al. (2012) Stochastic Volatility Models Including Open, Close, High and Low Prices. Quantitative Finance, 12, 199-212.
https://doi.org/10.1080/14697688.2010.492233
[12]  Kumar, D. and Maheswaran, S. (2014) Modeling and Forecasting the Additive Bias Corrected Extreme Value Volatility Estimator. International Review of Financial Analysis, 34, 166-176.
https://doi.org/10.1016/j.irfa.2014.06.002
[13]  Engle, R.F. (1982) Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica: Journal of the Econometric Society, 50, 987-1007.
https://doi.org/10.2307/1912773
[14]  Bollerslev, T. (1986) Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31, 307-327.
https://doi.org/10.1016/0304-4076(86)90063-1
[15]  Engle, R.F. and Bollerslev, T. (1986) Modelling the Persistence of Conditional Variances. Econometric Reviews, 5, 1-50.
https://doi.org/10.1080/07474938608800095
[16]  Baillie, R.T., Bollerslev, T. and Mikkelsen, H.O. (1996) Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 74, 3-30.
https://doi.org/10.1016/S0304-4076(95)01749-6
[17]  Nelson, D.B. (1991) Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica: Journal of the Econometric Society, 59, 347-370.
https://doi.org/10.2307/2938260
[18]  Glosten, L.R., Jagannathan, R. and Runkle, D.E. (1993) On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. The Journal of Finance, 48, 1779-1801.
https://doi.org/10.1111/j.1540-6261.1993.tb05128.x
[19]  Ding, Z., Granger, C.W. and Engle, R.F. (1993) A Long Memory Property of Stock Market Returns and a New Model. Journal of Empirical Finance, 1, 83-106.
https://doi.org/10.1016/0927-5398(93)90006-D
[20]  Bollerslev, T. and Ole Mikkelsen, H. (1996) Modeling and Pricing Long Memory in Stock Market Volatility. Journal of Econometrics, 73, 151-184.
https://doi.org/10.1016/0304-4076(95)01736-4
[21]  Tse, Y.K. (1998) The Conditional Heteroscedasticity of the Yen-Dollar Exchange Rate. Journal of Applied Econometrics, 13, 49-55.
https://doi.org/10.1002/(SICI)1099-1255(199801/02)13:1<49::AID-JAE459>3.0.CO;2-O
[22]  Clark, P.K. (1973) A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices. Econometrica: Journal of the Econometric Society, 41, 135-155.
https://doi.org/10.2307/1913889
[23]  Taylor, S.J. (1986) Modelling Financial Time Series. 2nd Edition, John Wiley and Sons, Hoboken.
[24]  Chou, R.Y. (2005) Forecasting Financial Volatilities with Extreme Values: The Conditional Autoregressive Range (CARR) Model. Journal of Money, Credit and Banking, 37, 561-582.
https://doi.org/10.1353/mcb.2005.0027
[25]  Brandt, M.W. and Jones, C.S. (2006) Volatility Forecasting with Range-Based EGARCH Models. Journal of Business & Economic Statistics, 24, 470-486.
https://doi.org/10.1198/073500106000000206
[26]  Chen, C.W., Gerlach, R. and Lin, E.M. (2008) Volatility Forecasting Using Threshold Heteroskedastic Models of the Intra-Day Range. Computational Statistics & Data Analysis, 52, 2990-3010.
https://doi.org/10.1016/j.csda.2007.08.002
[27]  Chiang, M.-H. and Wang, L.-M. (2011) Volatility Contagion: A Range-Based Volatility Approach. Journal of Econometrics, 165, 175-189.
https://doi.org/10.1016/j.jeconom.2011.07.004
[28]  Li, H. and Hong, Y. (2011) Financial Volatility Forecasting with Range-Based Autoregressive Volatility Model. Finance Research Letters, 8, 69-76.
https://doi.org/10.1016/j.frl.2010.12.002
[29]  Chan, J.S., et al. (2012) A Bayesian Conditional Autoregressive Geometric Process Model for Range Data. Computational Statistics & Data Analysis, 56, 3006-3019.
https://doi.org/10.1016/j.csda.2011.01.006
[30]  Kumar, D. (2015) Sudden Changes in Extreme Value Volatility Estimator: Modeling and Forecasting with Economic Significance Analysis. Economic Modelling, 49, 354-371.
https://doi.org/10.1016/j.econmod.2015.05.001
[31]  Kumar, D. (2016) Sudden Breaks in Drift-Independent Volatility Estimator Based on Multiple Periods Open, High, Low, and Close Prices. IIMB Management Review, 28, 31-42.
https://doi.org/10.1016/j.iimb.2016.02.001
[32]  Kumar, D. (2016) Sudden Changes in Crude Oil Price Volatility: An Application of Extreme Value Volatility Estimator. American Journal of Finance and Accounting, 4, 215-234.
https://doi.org/10.1504/AJFA.2016.080717
[33]  Kumar, D. (2017) Forecasting Energy Futures Volatility Based on the Unbiased Extreme Value Volatility Estimator. IIMB Management Review, 29, 294-310.
https://doi.org/10.1016/j.iimb.2017.11.002
[34]  Kumar, D. (2017) Structural Breaks in Unbiased Volatility Estimator: Modeling and Forecasting. Journal of Prediction Markets, 11, 399-421.
[35]  Kumar, D. (2017) Modeling and Forecasting Unbiased Extreme Value Volatility Estimator in Presence of Leverage Effect. Journal of Quantitative Economics, 1-23.
https://doi.org/10.1007/s40953-017-0085-4
[36]  Corsi, F. (2009) A Simple Approximate Long-Memory Model of Realized Volatility. Journal of Financial Econometrics, 7, 174-196.
https://doi.org/10.1093/jjfinec/nbp001
[37]  Hansen, P.R. (2005) A Test for Superior Predictive Ability. Journal of Business & Economic Statistics, 23, 365-380.
https://doi.org/10.1198/073500105000000063

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