Modelling and. Forecasting. High Frequency. Financial Data. Stavros Degiannakis and Christos Floros. palgrave. macmillan

Transcription

1 Modelling and Forecasting High Frequency Financial Data Stavros Degiannakis and Christos Floros palgrave macmillan

2 Contents List offigures List of Tables Acknowledgments List of Symbols and Operators xi xiv xvii xviii 1 Introduction to High Frequency Financial Modelling 1 1 The role of high frequency trading 2 2 Modelling volatility 10 3 Realized volatility 11 4 Volatility forecasting using high frequency data 14 5 Volatility evidence 14 6 Market microstructure 15 2 Intraday Realized Volatility Measures 24 1 The theoretical framework behind the realized volatility 24 2 Theory of ultra-high frequency volatility modelling 27 3 Equidistant price observations Linear Interpolation method Previous tick method 32 4 Methods of measuring realized volatility Conditional - inter-day - Variance Realized variance Price ränge Model-based duration Multiple grids Scaled realized ränge Price jumps Microstructure frictions Autocorrelation of intraday returns Interday adjustments 38 5 Simulating the realized volatility 42 6 Optimal sampling frequency 47 3 Methods of Volatility Estimation and Forecasting 58 1 Daily volatility models - review 58 vii

3 viii f Contents 1.1 ARCH(cj) model D9 1.2 GARCH(p,q) model APARCH(p, q) model FIGARCH(p, <i, q) model FIAPARCH(p,d,g) model Other methods of interday volatility modelling 61 2 Intraday volatility models: review ARFIMA(WJ) model ARFIMA(M',Z)-GARCH(p,<j) model HAR-RV model HAR-sqRV model HAR-GARCH(p,q) model Other methods of intraday volatility modelling 64 3 Volatility forecasting One-step-ahead volatility forecasting: Interday volatility models Daily volatility models: program construction One-step-ahead volatility forecasting: intraday volatility models Intraday volatility models: program construction 70 4 The construction ofloss functions Evaluation or loss functions Information criteria Loss functions depend on the aim of a specificapplication Multiple Model Comparison and Hypothesis Framework Construction Statistical methods of comparing the forecasting ability of models Diebold and Mariano test of equal forecast accuracy III 1.2 Reality check for data snooping III 1.3 Superior Predictive Ability test SPEC model selection method Theoretical framework: distribution functions A framework to compare the predictive ability of two competing models A framework to compare the predictive ability of n competing models Generic model Regression model Regression model with time varying conditional variance Fractionally integrated ARMA model with time varying conditional variance Intraday realized volatility application 123

4 Contents f ix 6 Simulate the SPEC criterion ARMA( 1,0) Simulation Repeat the Simulation Intraday simulated process Realized Volatility Forecasting: Applications Measuring realized volatility Volatility signature plot Interday adjustment of the realized volatility Distributional properties of realized volatility Forecasting realized volatility Programs construction Realized volatility forecasts comparison: SPEC criterion Logarithmic realized volatility forecasts comparison: SPA and DM Tests SPAtest DM test Recent Methods: A Review Modelling jumps Jump volatility measure and jump tests Daily jump tests Intraday jump tests Using OxMetrics (Re@lized under G@RCH 6.1) The RealGARCH model Realized GARCH forecasting Leverage effect Realized EGARCH Volatility forecasting with HAR-RV-J and HEAVY models The HAR-RV-J model The HEAVY model Financial risk measurements The method Intraday Hedge Ratios and Option Pricing Introduction to intraday hedge ratios Definition of hedge ratios BEKK model Asymmetrie BEKK model Constant Conditional Correlation (CCC) model Dynamic Conditional Correlation (DCC) model Estimation of the models Data Estimated hedge ratios 253

5 x J Contents 5 Hedging effectiveness Other models for intraday hedge ratios Introduction to intraday option pricings Price movement models The approach of Merton The approach of Scalas and Politi Relation between the distributions of the epochs and durations Price movement Option pricing The approach of Merton The approach of Scalas and Politi Time t is an epoch Time f is not an epoch Other models for intraday option pricing 269 Index 274