Modelling and Forecasting High Frequency Financial Data (eBook)

Dr. Christos Floros (Crete, Greece) is Professor of Finance at the Technological Educational Institute of Crete and Hellenic Open University (Greece). His main research interests include behavioural finance, financial derivatives (futures and options markets), financial econometrics (forecasting realized volatility, VaR modelling) and empirical banking (efficiency, competition and profitability). He has published extensively in academic journals and is the Editor-in-Chief of the International Journal of Financial Markets and Derivatives (IJFMD) and Editor of the International Journal of Computational Economics and Econometrics (IJCEE). He has been involved in a number of research funded projects including a Marie Curie project on 'Volatility forecasting evaluation based on loss function with well-defined multivariate distributional form and ultra-high frequency datasets (as co-ordinator). Christos has presented several papers at international academic conferences in the UK, Greece, Portugal, Italy, France, Ireland, and Spain, and is a Fellow of the Higher Education Academy (UK). Dr. Stavros Degiannakis is Assistant Professor in the Department of Economic and Regional Development of Panteion University of Social and Political Sciences. He has taught at various Universities including the Athens University of Economics and Business and the Hellenic Open University, Greece, in subjects such as statistics, econometrics, time series, data analysis and quantitative techniques. He has also served as econometrician for companies in the private and public sector (the Bank of Greece, the University of Portsmouth, the Economic Chamber of Greece, Inventive, the Hellenic Parliament, and Profile). He has served as a referee in more than 30 international journals, such as the Journal of Applied Econometrics, the Journal of Banking and Finance, and the Journal of Applied Statistics. His research interests are in the areas of applied and theoretical financial econometrics (ultra-high frequency data analysis, macro-finance modelling, option pricing, risk modelling) and statistics (marketing metrics, multivariate distributions, forecasting ability, time series analysis). Dr. Stavros Degiannakis received his PhD in Statistics from Athens University of Economics and Business. He graduated from the Athens University of Economics and Business, where he completed his studies in Statistics, and holds a M.Sc. degree in Econometrics from the University of Essex.

Cover 1
Half-Title 2
Title 4
Copyright 5
Dedication 6
Contents 8
List of Figures 12
List of Tables 15
Acknowledgments 18
List of Symbols and Operators 19
1 Introduction to High Frequency Financial Modelling 24
1 The role of high frequency trading 25
2 Modelling volatility 33
3 Realized volatility 34
4 Volatility forecasting using high frequency data 37
5 Volatility evidence 37
6 Market microstructure 38
2 Intraday Realized Volatility Measures 47
1 The theoretical framework behind the realized volatility 47
2 Theory of ultra-high frequency volatility modelling 50
3 Equidistant price observations 54
3.1 Linear interpolation method 54
3.2 Previous tick method 55
4 Methods of measuring realized volatility 55
4.1 Conditional – inter-day –Variance 55
4.2 Realized variance 57
4.3 Price range 58
4.4 Model-based duration. 60
4.5 Multiple grids 60
4.6 Scaled realized range 60
4.7 Price jumps 60
4.8 Microstructure frictions 60
4.9 Autocorrelation of intraday returns 61
4.10 Interday adjustments 61
5 Simulating the realized volatility 65
6 Optimal sampling frequency 70
3 Methods of Volatility Estimation and Forecasting 81
1 Daily volatilitymodels – review 81
1.1 ARCH(q)model 82
1.2 GARCH(p,q)model 82
1.3 APARCH(p,q)model 83
1.4 FIGARCH(p,d,q)model 83
1.5 FIAPARCH(p,d,q)model 83
1.6 Other methods of interday volatility modelling 84
2 Intraday volatility models: review 84
2.1 ARFIMA(k,d', l)model 84
2.2 ARFIMA(k,d', l)- GARCH(p,q)model 85
2.3 HAR-RVmodel 85
2.4 HAR-sqRVmodel 86
2.5 HAR-GARCH(p,q)model 86
2.6 Other methods of intraday volatility modelling 87
3 Volatility forecasting 87
3.1 One-step-ahead volatility forecasting: Interday volatility models 87
3.2 Daily volatility models: program construction 90
3.3 One-step-ahead volatility forecasting: intraday volatility models 90
3.4 Intraday volatility models: program construction 93
4 The construction of loss functions 93
4.1 Evaluation or loss functions 93
4.2 Information criteria 95
4.3 Loss functions depend on the aim of a specific application 96
4 Multiple Model Comparison and Hypothesis Framework Construction 133
1 Statistical methods of comparing the forecasting ability of models 133
1.1 Diebold and Mariano test of equal forecast accuracy 134
1.2 Reality check for data snooping 134
1.3 Superior Predictive Ability test 135
1.4 SPEC model selection method 135
2 Theoretical framework: distribution functions 136
3 A framework to compare the predictive ability of two competing models 138
4 A framework to compare the predictive ability of n competing models 142
4.1 Generic model 142
4.2 Regression model 144
4.3 Regression model with time varying conditional variance 144
4.4 Fractionally integrated ARMA model with time varying conditional variance 145
5 Intraday realized volatility application. 146
6 Simulate the SPEC criterion 151
6.1 ARMA(1,0) simulation 151
6.2 Repeat the simulation 153
6.3 Intraday simulated process 156
5 Realized Volatility Forecasting: Applications 184
1 Measuring realized volatility 184
1.1 Volatility signature plot 185
1.2 Interday adjustment of the realized volatility 188
1.3 Distributional properties of realized volatility 197
2 Forecasting realized volatility 199
3 Programs construction 201
4 Realized volatility forecasts comparison: SPEC criterion 213
5 Logarithmic realized volatility forecasts comparison: SPA and DM Tests 223
5.1 SPA test 223
5.2 DM test 225
6 Recent Methods: A Review 240
1 Modelling jumps 240
1.1 Jump volatility measure and jump tests 241
1.2 Daily jump tests 242
1.3 Intraday jump tests 243
1.4 Using OxMetrics (Re@lized under G@RCH 6.1) 244
2 The RealGARCH model 253
2.1 Realized GARCH forecasting 255
2.2 Leverage effect 257
2.3 Realized EGARCH 257
3 Volatility forecasting with HAR-RV-J and HEAVY models 258
3.1 The HAR-RV-J model 258
3.2 The HEAVY model 259
4 Financial risk measurements 261
4.1 The method 261
7 Intraday Hedge Ratios and Option Pricing 266
1 Introduction to intraday hedge ratios 266
2 Definition of hedge ratios 269
2.1 BEKKmodel 271
2.2 Asymmetric BEKKmodel 271
2.3 Constant Conditional Correlation (CCC) model 272
2.4 DynamicConditionalCorrelation (DCC)model 273
2.5 Estimation of themodels 274
3 Data 274
4 Estimated hedge ratios 276
5 Hedging effectiveness 279
6 Other models for intraday hedge ratios 282
7 Introduction to intraday option pricings 282
8 Price movement models 283
8.1 The approach of Merton 284
8.2 The approach of Scalas and Politi 284
8.3 Relation between the distributions of the epochs and durations 285
8.4 Price movement 286
9 Option pricing 288
9.1 The approach ofMerton 288
9.2 The approach of Scalas and Politi 288
9.3 Time t is an epoch 289
9.4 Time t is not an epoch 290
9.5 Other models for intraday option pricing 292
Index 297