Skip to main content

ARCH Models for Financial Applications

ARCH Models for Financial Applications

Evdokia Xekalaki, Stavros Degiannakis

ISBN: 978-0-470-68801-4

Mar 2010

558 pages


Autoregressive Conditional Heteroskedastic (ARCH) processes are used in finance to model asset price volatility over time. This book introduces both the theory and applications of ARCH models and provides the basic theoretical and empirical background, before proceeding to more advanced issues and applications. The Authors provide coverage of the recent developments in ARCH modelling which can be implemented using econometric software, model construction, fitting and forecasting and model evaluation and selection.

Key Features:

  • Presents a comprehensive overview of both the theory and the practical applications of ARCH, an increasingly popular financial modelling technique.
  • Assumes no prior knowledge of ARCH models; the basics such as model construction are introduced, before proceeding to more complex applications such as value-at-risk, option pricing and model evaluation.
  • Uses empirical examples to demonstrate how the recent developments in ARCH can be implemented.
  • Provides step-by-step instructive examples, using econometric software, such as Econometric Views and the G@RCH module for the Ox software package, used in Estimating and Forecasting ARCH Models.
  • Accompanied by a CD-ROM containing links to the software as well as the datasets used in the examples.

Aimed at readers wishing to gain an aptitude in the applications of financial econometric modelling with a focus on practical implementation, via applications to real data and via examples worked with econometrics packages.



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.


Author Index.

Subject Index.

"Numerous articles on the Autoregressive Conditional Heteroskedastic (ARCH) process, an increasingly popular financial modeling technique, exist in various international journals. Now Xekalaki and Degiannakis (both statistics, Athens U. of Economics and Business, Greece) provide a thorough treatment of the ARCH theory and its practical applications, in a textbook for postgraduate and final-year undergraduate students which could serve as reference work for academics and financial market professionals." (Book News Inc, November 2010)