1. bookVolume 6 (2016): Issue 3 (July 2016)
Journal Details
First Published
30 Dec 2014
Publication timeframe
4 times per year
access type Open Access

An Analysis of the Performance of Genetic Programming for Realised Volatility Forecasting

Published Online: 10 Jun 2016
Page range: 155 - 172
Journal Details
First Published
30 Dec 2014
Publication timeframe
4 times per year

Traditionally, the volatility of daily returns in financial markets is modeled autoregressively using a time-series of lagged information. These autoregressive models exploit stylised empirical properties of volatility such as strong persistence, mean reversion and asymmetric dependence on lagged returns. While these methods can produce good forecasts, the approach is in essence atheoretical as it provides no insight into the nature of the causal factors and how they affect volatility. Many plausible explanatory variables relating market conditions and volatility have been identified in various studies but despite the volume of research, we lack a clear theoretical framework that links these factors together. This setting of a theory-weak environment suggests a useful role for powerful model induction methodologies such as Genetic Programming (GP). This study forecasts one-day ahead realised volatility (RV) using a GP methodology that incorporates information on market conditions including trading volume, number of transactions, bid-ask spread, average trading duration (waiting time between trades) and implied volatility. The forecasting performance from the evolved GP models is found to be significantly better than those numbers of benchmark forecasting models drawn from the finance literature, namely, the heterogeneous autoregressive (HAR) model, the generalized autoregressive conditional heteroscedasticity (GARCH) model, and a stepwise linear regression model (SR). Given the practical importance of improved forecasting performance for realised volatility this result is of significance for practitioners in financial markets.


[1] R.F. Engle. GARCH 101: The use of ARCH/GARCH models in applied econometrics. Journal of Economic Perspectives, vol. 14, pp. 157-168, 2001.Search in Google Scholar

[2] N. Shephard. Stochastic Volatility. Economics Group, Nuffield College, University of Oxford, Economics Papers, 2005.Search in Google Scholar

[3] W.K.H. Fung and D.A. Hsieh. Empirical Analysis of Implied Volatility: Stock, Bonds and Currencies, presented at the 4th Annual Conference of the Financial Operations Research Center, University of Warwick, Coventry, England, 1991.Search in Google Scholar

[4] F.X. Diebold and R. Mariano. Comparing Predictive Accuracy. Journal of Business and Economic Statistics, vol. 13, pp. 253-265, 1995.Search in Google Scholar

[5] S.H. Poon and C.W.J. Granger. Forecasting Volatility in Financial Markets: A Review. Journal of Economic Literature, vol. XLI, pp. 478-539, 2003.Search in Google Scholar

[6] J.R. Koza. Genetic Programming. Massachusetts: MIT Press, 1992.Search in Google Scholar

[7] J. R. Koza. Genetic Programming II. Massachusetts: MIT Press, 1994.Search in Google Scholar

[8] Poli R., Landon W.B. and McPhee N.F (2008) A field guide to genetic programming, Published via http://lulu.com and freely available: http://www.gp-field-guide.org.ukSearch in Google Scholar

[9] S.-H. Chen and C.H. Yeh. Using Genetic Programming to Model Volatility in Financial Time Series: the Case of Nikkei 225 and S&P 500. in Proc. of the 4th JAFEE International Conference on Investments and Derivatives(JIC’97), Aoyoma Gakuin University, Tokyo, Japan, July 29-31, 1997, pp.288-306.Search in Google Scholar

[10] R.F. Engle. The Econometrics of Ultra High Frequency Data. Econometrica, vol. 68, pp. 1-22, 2000.Search in Google Scholar

[11] G. Zumbach, O.V. Pictet and O. Masutti. (2001) Genetic Programming with Syntactic Restrictions Applied to Financial Volatility Forecasting. Olsen & Associates Working Paper, [online] Paper No. GOZ.2000-07-28. Available: http://ssrn.com/abstract=269189 [15 Dec. 2006].Search in Google Scholar

[12] C.J. Neely and P.A. Weller Predicting Exchange Rate Volatility: Genetic Programming Versus GARCH and RiskMetricsTM. The Federal Reserve Bank of St. Louis, May/June, 2002.Search in Google Scholar

[13] I. Ma, T. Wong , T. Sankar and R. Siu. Forecasting the Volatility of a Financial Index by Wavelet Transform and Evolutionary Algorithm. in Proc. of the 2004 IEEE International Conference on Systems, Man and Cybernetics, pp. 5824-5829, 2004.Search in Google Scholar

[14] S. B. Hamida and R. Cont. Recovering Volatility from Option Prices by Evolutionary Optimization. Journal of Computational Finance, vol. 8, No. 4, Summer 2005.Search in Google Scholar

[15] W. Abdelmalek, S. B. Hamida and F. Abid. (2009). Selecting the Best Forecasting-Implied Volatility Model Using Genetic Programming. Journal of Applied Mathematics and Decision Sciences, [online]. vol. 2009, Article ID 179230. Available: http://www.hindawi.com/journals/ads/2009/179230/ [17 Sep.2011].Search in Google Scholar

[16] H.M. Wu and W.C. Guo. Asset Price Volatility and Trading Volume with Rational Beliefs. Economic Theory, vol. 23, no. 4, pp. 795-829, Jun. 2004.Search in Google Scholar

[17] H.C. Chena and J.Wu. Return Volatility and the Intraday Behavior of Market Liquidity without Market Makers: Evidence from the Taiwan Futures Market. International Research Journal of Finance and Economics, Issue 17, pp. 117-128, Jul. 2008.Search in Google Scholar

[18] S.J. Taylor. Forecasting the Volatility of Currency Exchange Rates. International Journal of Forecasting, vol. 3, pp. 159-170, 1987.Search in Google Scholar

[19] L.R. Glosten, R. Jagannathan and D.E. Runkle. On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. The Journal of Finance, vol. 48, no. 5, pp. 1779-1801, 1993.Search in Google Scholar

[20] M. Ammann, D. Skovmand and M. Verhofen. Implied and Realized Volatility in the Cross-Section of Equity Options. International Journal of Theoretical and Applied Finance, vol. 12, issue 6, pp. 745-765, 2009.Search in Google Scholar

[21] G.H.K. Wang and J. Yau. Trading Volume, Bid- Ask Spread, and Price Volatility in Futures Markets. Journal of Futures Markets, vol. 20, issue 10, pp. 943-970, 2000.Search in Google Scholar

[22] M. McAleer and M.C. Medeiros. Realized Volatility: A Review. Econometric Reviews, vol. 27(1-3), pp. 10-45, 2008.Search in Google Scholar

[23] T.G. Andersen, T. Bollerslev, F.X. Diebold and P. Labys. Modeling and Forecasting Realized Volatility. Econometrica, vol. 71, pp. 529-626, 2003.Search in Google Scholar

[24] T.G. Andersen and T. Bollerslev. Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts. International Economic Review, vol. 39, no. 4, pp. 885-905, 1998.Search in Google Scholar

[25] N.M.P.C. Areal and S.J. Taylor. The Realized Volatility of FTSE 100 Futures Prices. Journal of Futures Markets, vol. 22, issue 7, pp. 627-648, 2000.Search in Google Scholar

[26] D.D. Thomakos and T.Wang. Realized Volatility in the Futures Markets. Journal of Empirical Finance, vol. 10, pp. 321-353, 2003.Search in Google Scholar

[27] F. Corsi. A Simple Long Memory Model of Realized Volatility. Working Paper, University of Southern Switzerland, vol. 71, pp.529-626, 2003.Search in Google Scholar

[28] Y. Aït-Sahalia and L. Mancini. Out of Sample Forecasts of Quadratic Variation. Journal of Econometrics, vol. 147, pp. 17-33, 2008.Search in Google Scholar

[29] L. Xiao. Realized Volatility Forecasting: Empirical Evidence from Stock Market Indices and Exchange Rates. Applied Financial Economics, vol. 23, pp. 57-69, 2013.Search in Google Scholar

[30] F. Corsi, S. Miittnik, Ch. Pigorsch and U. Pigorsch. The Volatility of Realized Volatility. Econometric Reviews, vol. 27, pp. 46-78, 2008.Search in Google Scholar

[31] T.G. Andersen, T. Bollerslev and F.X. Diebold. Roughing It Up: Including Jump Components in the Measurement, Modeling and Forecasting of Return Volatility. Review of Econometrics and Statistics, vol. 89, pp. 701-720, 2007.Search in Google Scholar

[32] F. Corsi. A Simple Approximate Long-Memory Model of Realized Volatility. Journal of Financial Econometrics, vol. 7, no. 2, pp. 174-196, 2009.Search in Google Scholar

[33] A.M. Fuertes, M. Izzeldin and E. Kalotychou. On Forecasting Daily Stock Volatility: The Role of Intraday Information and Market Conditions. International Journal of Forecasting, vol. 25, pp. 259-281, 2009.Search in Google Scholar

[34] N.K. Léon. (2008) The Effects of Interest Rates Volatility on Stock Returns and Volatility: Evidence from Korea. International Research Journal of Finance and Economics, [online]. ISSN 1450-2887, issue 14. Available: http://www.eurojournals.com/finance.htm[1 Jan. 2012].Search in Google Scholar

[35] N. Zafar, S.F. Urooj and T.K. Durrani. (2008) Interest Rate Volatility and Stock Return and Volatility. European Journal of Economics, Finance and Administrative Sciences, [online]. ISSN 1450-2887, Issue 14. Available: http://www.eurojournals.com [1 Jan. 2012].Search in Google Scholar

[36] S. Rahman, C.F. Lee and K.P. Ang. Intraday Return Volatility Process: Evidence from NASDAQ Stocks. Review of Quantitative Finance and Accounting, vol. 19, pp. 155-180, 2002.Search in Google Scholar

[37] E. Kalotychou and S.K. Staikouras. Volatility and Trading Activity in Short Sterling Futures. Applied Economics, vol.38, no. 9, pp. 997-1005, 2006.Search in Google Scholar

[38] C.M. Jones and G. Kaul. Transactions, Volume, and Volatility. The Review of Financial Studies, vol. 7, no. 4, pp. 631-651, 1994.Search in Google Scholar

[39] L.R. Glosten, R. Jagannathan and D.E. Runkle. On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. The Journal of Finance, vol. 48, no. 5, pp. 1779-1801, 1993.Search in Google Scholar

[40] A.F. Darrat, S. Rahman and M. Zhong. Intraday Trading Volume and Return Volatility of the DJIA Stocks: A Note. Journal of Banking & Finance, vol. 27, pp. 2035-2043, 2003.Search in Google Scholar

[41] C. Brooks. Predicting Stock Index Volatility: Can Market Volume Help? Journal of Forecasting, vol. 17, pp. 59-80, 1998.Search in Google Scholar

[42] Research & Planning Department.(2006, Oct.) Global Exchange Derivative Volumes - A Statistical Overview. Exchange Newsletter (Hong Kong, China). [Online] Available: http:www.hkex.com.hk/eng/newsconsul/newsltr/2011newsletter.htm [15 Jul. 2013].Search in Google Scholar

[43] R.F. Engle and G.M. Gallo. A Multiple Indicators Model for Volatility Using Intra-daily Data. Journal of Econometrics, vol. 131, pp. 3-27, 2006.Search in Google Scholar

[44] G. Donaldson and M. Kamstra. Volatility Forecasts, Trading Volume, and the ARCH versus Option-Implied Volatility Trade-off. Journal of Financial Research, Southern Finance Association & Southwestern Finance Association, vol.28, no. 4, pp.519-538, 2005.Search in Google Scholar

[45] C. Christiansen, M. Schmeling and A. Schrimpf. A Comprehensive Look at Financial Volatility Prediction by Economic Variables. BIS Working Paper, no. 374, pp. 41-45, 2008.Search in Google Scholar

[46] S. Li and Q. Yang. The Relationship between Implied and Realized Volatility: Evidence from the Australian Stock Index Option Market. Rev. Quant Finance Account, vol. 32, pp. 405-419, 2009.Search in Google Scholar

[47] J Shu and J.E. Zhang. The Relationship between Implied and Realized Volatility of S&P 500 Index. WILMOTT Magazine, Technical Article 4, pp. 83-91, 2003. Search in Google Scholar

[48] B. Blair, S.H. Poon and S. J. Taylor. Forecasting S&P 100 Volatility: the Incremental Information Content of Implied Volatilities and High Frequency Index Returns. Journal of Econometrics, vol. 105 (1), pp. 5-26, 2001.Search in Google Scholar

[49] B.J. Christensen and N.R. Prabhala. The Relation Between Implied and Realized Volatility. Journal of Financial Economics, vol. 50, pp. 125-150, 1998.Search in Google Scholar

[50] L. Canina and S. Figlewski. The Informational Content of Implied Volatility. The Review of Financial Studies, vol. 6, no. 3, pp. 659-681, 1993.Search in Google Scholar

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