ARCH Models for Financial Applications

Notation.

1 What is an ARCH process?

1.1 Introduction.

1.2 The Autoregressive Conditionally Heteroskedastic Process.

1.3 The Leverage Effect.

1.4 The Non-trading Period Effect.

1.5 Non-synchronous Trading Effect.

1.6 The Relationship between Conditional Variance and Conditional Mean.

2 ARCH Volatility Specifications.

2.1 Model Specifications.

2.2 Methods of Estimation.

2.3. Estimating the GARCH Model with EViews 6: An Empirical Example..

2.4. Asymmetric Conditional Volatility Specifications.

2.5. Simulating ARCH Models Using EViews.

2.6. Estimating Asymmetric ARCH Models with G@RCH 4.2 OxMetrics – An Empirical Example..

2.7. Misspecification Tests.

2.8 Other ARCH Volatility Specifications.

2.9 Other Methods of Volatility Modeling.

2.10 Interpretation of the ARCH Process.

3 Fractionally Integrated ARCH Models.

3.1 Fractionally Integrated ARCH Model Specifications.

3.2 Estimating Fractionally Integrated ARCH Models Using G@RCH 4.2 OxMetrics – An Empirical Example.

3.3 A More Detailed Investigation of the Normality of the Standardized Residuals – Goodness-of-fit Tests.

4 Volatility Forecasting: An Empirical Example Using EViews 6.

4.1 One-step-ahead Volatility Forecasting.

4.2 Ten-step-ahead Volatility Forecasting.

5 Other Distributional Assumptions.

5.1 Non-Normally Distributed Standardized Innovations.

5.2 Estimating ARCH Models with Non-Normally Distributed Standardized Innovations Using G@RCH 4.2 OxMetrics – An Empirical Example.

5.3 Estimating ARCH Models with Non-Normally Distributed Standardized Innovations Using EViews 6 – An Empirical Example.

5.4 Estimating ARCH Models with Non-Normally Distributed Standardized Innovations Using EViews 6 – The LogL Object.

6 Volatility Forecasting: An Empirical Example Using G@RCH Ox.

7 Intra-Day Realized Volatility Models.

7.1 Realized Volatility.

7.2 Intra-Day Volatility Models.

7.3 Intra-Day Realized Volatility & ARFIMAX Models in G@RCH 4.2 OxMetrics – An Empirical example.

8 Applications in Value-at-Risk, Expected Shortfalls, Options Pricing.

8.1 One-day-ahead Value-at-Risk Forecasting.

8.2 One-day-ahead Expected Shortfalls Forecasting.

8.3 FTSE100 Index: One-step-ahead Value-at-Risk and Expected Shortfall Forecasting.

8.4 Multi-period Value-at-Risk and Expected Shortfalls Forecasting.

8.5 ARCH Volatility Forecasts in Black and Scholes Option Pricing.

8.6 ARCH Option Pricing Formulas.

9 Implied Volatility Indices and ARCH Models.

9.1 Implied Volatility.

9.2 The VIX Index.

9.3 The Implied Volatility Index as an Explanatory Variable.

9.4 ARFIMAX Modeling for Implied Volatility Index.

10 ARCH Model Evaluation and Selection.

10.1 Evaluation of ARCH Models.

10.2 Selection of ARCH Models.

10.3 Application of Loss Functions as Methods of Model Selection..

10.4 The SPA Test for VaR and Expected Shortfalls.

11 Multivariate ARCH Models.

11.1 Model Specifications.

11.2 Maximum Likelihood Estimation.

11.3 Estimating Multivariate ARCH Models Using EViews 6.

11.4 Estimating Multivariate ARCH Models Using G@RCH 5.0.

11.5 Evaluation of Multivariate ARCH Models.

References.

Author Index.

Subject Index.