ARCH Models and Financial Applications

1 Introduction.- 1.1 The Development of ARCH Models.- 1.2 Book Content.- 2 Linear and Nonlinear Processes.- 2.1 Stochastic Processes.- 2.2 Weak and Strict Stationarity.- 2.3 A Few Examples.- 2.4 Nonlinearities.- 2.5 Exercises.- 3 Univariate ARCH Models.- 3.1 A Heteroscedastic Model of Order One.- 3.2 General Properties of ARCH Processes.- 3.3 Exercises.- 4 Estimation and Tests.- 4.1 Pseudo Maximum Likelihood Estimation.- 4.2 Two Step Estimation Procedures.- 4.3 Forecast Intervals.- 4.4 Homoscedasticity Test.- 4.5 The Test Statistic Interpretation.- Appendix 4.1: Matrices I and J.- Appendix 4.2: Derivatives of the Log-Likelihood Function and Information Matrix for a Regression Model with ARCH Errors.- 4.6 Exercises.- 5 Some Applications of Univariate ARCH Models.- 5.1 Leptokurtic Aspects of Financial Series and Aggregation.- 5.2 ARCH Processes as an Approximation of Continuous Time Processes.- 5.3 The Random Walk Hypothesis.- 5.4 Threshold Models.- 5.5 Integrated Models.- 5.6 Exercises.- 6 Multivariate ARCH Models.- 6.1 Unconstrained Models.- 6.2 Constrained Models.- 6.3 Estimation of Heteroscedastic Dynamic Models.- 7 Efficient Portfolios and Hedging Portfolios.- 7.1 Determination of an Efficient Portfolio.- 7.2 Properties of the Set of Efficient Portfolios.- 7.3 Asymmetric Information and Aggregation.- 7.4 Hedging Portfolios.- 7.5 Empirical Study of Performance Measures.- Appendix 1: Presentation in Terms of Utility.- Appendix 2: Moments of the Truncated Log-Normal Distribution.- Appendix 3: Asymptotic Properties of the Estimators.- 7.6 Exercises.- 8 Factor Models, Diversification and Efficiency.- 8.1 Factor Models.- 8.2 Arbitrage Theory.- 8.3 Efficiency Tests and Diversification.- 8.5 Exercises.- 9 Equilibrium Models.- 9.1 Capital Asset Pricing Model.- 9.2 Test of theCAPM.- 9.3 Examples of Structural Models.

Zusammenfassung
The ARMA models have limitations when applied to the field of financial and monetary economics. Financial time series present nonlinear dynamic characteristics and ARCH models offer an adaptive framework for this problem. This book surveys the work in this area from the perspective of statistical theory, financial models, and applications.