NSE Proposal

Forecasting Volalitity using High Frequency data

Introduction and scope of work The paper will be modeling and forecasting volatility (risk) for Indian Equity market. The widespread availability of databases recording the intraday price movements called high frequency (HF) data of financial assets (stocks, indexes, currencies, derivatives) has led to new developments in applied econometrics and quantitative finance. The focus of research will be on HF data since 2000. Advances in computer technology and data recording and storage have made these data sets increasingly accessible to researchers and have driven the data frequency to the ultimate limit for some financial markets: time stamped transaction-by-transaction or tick-by-tick data, referred to as ultra-high-frequency data by Engle (2000). HF data are also useful for studying various statistical properties of the variables, volatility in particular. Statistical properties like frequency of price revision, unit roots, correlation and volatility behavior will be measured and analysed. This will be an empirical study to assess the forecasting performance of a wide range of models for predicting volatility and VaR (value at risk) in the National Stock Exchange (NSE). Parametric models for financial asset returns volatility have undergone great development since the seminal autoregressive conditional heteroscedasticity (ARCH), and generalized ARCH (GARCH) models of Engle (1982) and Bollerslev (1986). The literature on this topic is very extensive; see, for instance, Bollerslev et al. (1992) and Bauwens et al. (2006) for comprehensive surveys on univariate and multivariate ARCH-type models. While GARCH model remains useful in capturing volatility clustering for high frequency returns, the intraday deterministic volatility seasonals need to be carefully accounted for before carrying out an analysis of the volatility dynamics (Mian, Adam (2001). Excellent surveys on the use of HF financial data sets in financial econometrics are provided by Andersen (2000), Campbell, Lo and MacKinlay (1997), Dacarogna et. al. (2001), Ghysels (2000), Goodhart (1991,1997) and O’Hara (1997), Gouri´eroux and Jasiak (2001), Lyons (2001), Tsay (2001), and Wood (2000). Thomas & Patnaik (2002) and Batra (2004) has studied behaviour in Indian Equity market using HF data also Bhanumurthy (2002) have analysed HF data on exchange rates in Indian scenario. Nath & Dalvi on HF data has tried to model volatility using various models and have shown which model is the best; using intraday returns at frequency interval of 1 minute. The paper will focus on various measures of modeling volatility and proposing benefits of a model based on HF data. Also forecasting will be done for future time period. HF data has insights which really drive market and asset prices. Volatility of asset returns is central to modern finance theory, and is widely used in asset pricing, portfolio selection, and risk management. Unlike other market variables like price changes and spread, the volatility is not directly observable and there is no unique method for estimating it. Model-based volatility measures include GARCH models, stochastic volatility models, or the volatility implied by options or other derivatives prices. Andersen et. al. (2001) proposes an alternative mode-free approach to estimate ex post realized volatility from squared returns within the volatility horizon. They prove that as the sampling frequency of returns approaches infinity, realized volatility measures are asymptotically free of measurement error. For daily volatility, they use 5-minute returns to construct daily realized volatilities. The time between consecutive events (defined as duration) is no longer constant, standard time series analysis techniques are inadequate when applied directly to these HF transaction data (Dionne, Duchesne, Maria (2005)). Also the empirical analyses of such data present a

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number of new and unique statistical challenges; this paper will highlight them too. Maybe more surprisingly, the high-frequency data also allow for much more accurate ex-post volatility measurements and modeling of the longer-run interdaily dynamic dependencies. The paper will model volatility using fractionally integrated autoregressive moving average (ARFIMA) models (Hardle, Hautsch, Pigorsch (2008)) and UHF (Ultra high frequency) GARCH model if data permits. Generally the empirical results show significant improvements in the point forecasts of volatility when using ARFIMA rather than GARCH-type models. Further, UHF-GARCH models (Dionne, Duchesne, Maria (2005)) have proved to be a good performer of out-of-sample predictions. The model developed in this study will be used to forecast volatility and returns for S&P CNX NIFTY key stocks. S&P CNX Nifty launched in April, 1996 is a well diversified 50 stock index accounting for 21 sectors of the economy. It is used for a variety of purposes such as benchmarking fund portfolios, index based derivatives and index funds. S&P CNX Nifty is owned and managed by India Index Services and Products Ltd. (IISL), which is a joint venture between NSE and CRISIL. IISL is India's first specialised company focused upon the index as a core product. IISL has Marketing and licensing agreement with Standard & Poor's (S&P), who are world leaders in index services. S&P CNX Nifty is computed using market capitalization weighted method, wherein the level of the index reflects the total market value of all the stocks in the index relative to a particular base period. The method also takes into account constituent changes in the index and importantly corporate actions such as stock splits, rights, etc without affecting the index value. Paper will also review sectoral interlinkages and correlations affecting volatility and returns. This will help in building a good forecasting model for volatility of Indian stocks. Data requirement Data on intraday trades at NSE will be used for the study. Data source will be Bloomberg or NSE for HF historical data of stocks traded at NSE. Econometric Methodology Traditional models like ARMA, GARCH and recently developed ARFIMA will be used to study volatility in the India equity market.

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References Campbell, Lo and MacKinlay (1997), Dacarogna et. al. (2001), Ghysels (2000), Goodhart and O’Hara (1997), Gouri´eroux and Jasiak (2001), Lyons (2001), Tsay (2001), and Wood (2000). Andersen, T. G. (2000), ‘Some reflections on analysis of high-frequency data’, Journal of Business Economics & Statistics 18(2). Andersen, T. G. & Bollerslev, T. (1997), ‘Intraday seasonality and volatility persistence in financial markets’, Journal of Empirical Finance 4, 115-58. Banerjee , Ashok & Sarkar, Sahadeb (2006), ‘Modeling daily volatility of the Indian stock market using intra-day data’, IIM Calcutta, WPS No. 588 Batra, Amita (2004), ‘Stock Return Volatility Patterns in India’, ICRIER Working Paper No. 124 Bauwens, Luc & Laurent, S & Peters, J. P. & Rombouts, J (2002), ‘Multivariate GARCH models and their Estimation,’ Computing in Economics and Finance, 19, Society for Computational Economics. Bhanumurthy, N. R. (2002), ‘Microstructures in the Indian Foreign Exchange Market’, at http://www.olsen.ch/fileadmin/Publications/Client_Papers//200212-Bhanumurthy-MicroIndianFX.pdf Bollerslev, T., Chou, R. Y. & Kroner, F (1992), ‘ARCH Modeling in Finance: A Review of the Theory and Empirical Evidence’, Journal of Econometrics, Vol.52, No.1, pp.5-59, 1992. Campbell, J. Y., Lo, A. W., and MacKinlay, A. C., 1997, The Econometrics of Financial Markets, Princeton University Press, New Jersey. Dacarogna, M. M., Gen¸cay, R., M¨uller, U. A., Olsen, R. B., and Pictet, O. V., 2001, An Introduction to High-Frequency Finance, Academic Press Dionne, Georges, Duchesne, Pierre & Pacurar, Maria (2005), ‘Intraday Value at Risk (IVaR) Using Tick-by-Tick Data with Application to the Toronto Stock Exchange’, School of Business Administration, Dalhousie University Easley, D., and O’Hara, M, 1992, ‘Time and the Process of Security Price Adjustment, Journal of Finance’, 47, 577-605 Engle, Robert F. (1996), ‘The Econometrics of ultra-high frequency data’, University of California, Discussion Paper 96-15 Engle, R.F. (2000), ‘The Econometrics of Ultra-High Frequency Data,’ Econometrica, 68, 1-22. Ghysels, E., 2000, ‘Some Econometric Recipes for High-Frequency Data Cooking’, Journal of Business and Economic Statistics, 18, 154-163

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Giot, P. (2000), Intraday value-at-risk, DP 2000/45, Centre for Operations Research and Econometrics. Goodhart, C. A. E. & Figliuoli, L. (1991), ‘Every minute counts in financial markets’, Journal of International Money and Finance 10, 23-52. Goodhart, C. A. E. & O'Hara, M. (1997), ‘High frequency data in financial markets: Issues and applications’, Journal of Empirical Finance 4, 73-114. Goodhart, C.A.E., and O’Hara, M, 1997, ‘High Frequency Data in Financial Markets: Issues and Applications’, Journal of Empirical Finance, 4, 73-114 Gouri´eroux, C., and Jasiak, J., 2001, Financial Econometrics: Problems, Models, and Methods, Princeton University Press, New Jersey Hardle, Wolfgang, Hautsch, Nikolaus & Pigorsch, Uta (2008), ‘Measuring and Modeling Risk Using High-Frequency Data’, SFB 649 Discussion Paper 2008-045 Lyons, R., 2001, The Microstructure Approach to Exchange Rates, MIT Press Mian, G. M. & Adam, C. M. (2001), ‘Volatility dynamics in high frequency financial data: an empirical investigation of the Australian equity returns’, Applied Financial Economics 11, 341-352 Nath, G. C. & Dalvi, Maoj (2008), ‘A suitable Volatility Measure in Indian Stock Market’, Available at SSRN: http://ssrn.com/abstract=1092743 Ñíguez, Trino-Manuel (2008), ‘Volatility and VaR forecasting in the Madrid Stock Exchange’, Span Econ Rev (2008) 10:169–196 NSE Factbook, http://nse-india.com/content/us/fact2007_sec1.pdf Patnaik, T. C. & Thomas, Susan, ‘High Frequency Data In Finance: A Study Of The Indian Intraday Equity Markets’, 2002, IGIDR Tsay, R. S., 2001, Analysis of Financial Time Series, John Wiley & Sons, Inc Wood, R. A., 2000, ‘Market Microstructure Research Databases: History and Projections’, Journal of Business and Economic Statistics, 18, 140-145 Yan, Bingcheng & Zivot, Eric (2003), ‘Analysis of High-Frequency Financial Data with S-Plus’, Department of Economics, University of Washington