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Inhalt

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.- 2.4.1 Portmanteau Statistic.- 2.4.2 Some Implications of the White Noise Hypothesis..- 2.5 Exercises.- 3 Univariate ARCH Models.- 3.1 A Heteroscedastic Model of Order One.- 3.1.1 Description of the Model.- 3.1.2 Properties of the Innovation Process ?.- 3.1.3 Properties of the Y Process.- 3.1.4 Distribution of the Error Process.- 3.2 General Properties of ARCH Processes.- 3.2.1 Various Extensions.- 3.2.2 Stationarity of a GARCH(p, q) Process.- 3.2.3 Kurtosis.- 3.2.4 Yule-Walker Equations for the Square of a GARCH Process.- 3.3 Exercises.- 4 Estimation and Tests.- 4.1 Pseudo Maximum Likelihood Estimation.- 4.1.1 Generalities.- 4.1.2 The i.i.d. case.- 4.1.3 Regression Model with Heteroscedastic Errors.- 4.1.4 Regression Model with ARCH Errors.- 4.1.5 Application to a GARCH Model.- 4.1.6 Stochastic Variance Model.- 4.2 Two Step Estimation Procedures.- 4.2.1 Description of the Procedures.- 4.2.2 Comparison of the Estimation Methods under Conditional Normality.- 4.2.3 Efficiency Loss Analysis.- 4.3 Forecast Intervals.- 4.4 Homoscedasticity Test.- 4.4.1 Regression Models with Heteroscedastic Errors.- 4.5 The Test Statistic Interpretation.- 4.5.1 Application to Regression Models with ARCH or GARCH Errors.- 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.- 5.1.1 The Normality Assumption.- 5.1.2 The Choice of a Time Unit.- 5.2 ARCH Processes as an Approximation of Continuous Time Processes.- 5.2.1 Stochastic Integrals.- 5.2.2 Stochastic Differential Equations.- 5.2.3 Some Equations and Their Solutions.- 5.2.4 Continuous and Discrete Time.- 5.2.5 Examples.- 5.2.6 Simulated Estimation Methods.- 5.3 The Random Walk Hypothesis.- 5.3.1 Description of the Hypothesis.- 5.3.2 The Classical Test Procedure of the Random Walk Hypothesis.- 5.3.3 Limitations of the Portmanteau Tests.- 5.3.4 Portmanteau Tests with Heteroscedasticity.- 5.4 Threshold Models.- 5.4.1 Definition and Stationarity Conditions.- 5.4.2 Homoscedasticity Test.- 5.4.3 Qualitative ARCH Models.- 5.4.4 Nonparametric Approaches.- 5.5 Integrated Models.- 5.5.1 The IGARCH(1,1) Model.- 5.5.2 The Persistence Effect.- 5.5.3 Weak and Strong Stationarity.- 5.5.4 Example.- 5.6 Exercises.- 6 Multivariate ARCH Models.- 6.1 Unconstrained Models.- 6.1.1 Multivariate GARCH Models.- 6.1.2 Positivity Constraints.- 6.1.3 Stability Conditions.- 6.1.4 An Example.- 6.1.5 Spectral Decompositions.- 6.2 Constrained Models.- 6.2.1 Diagonal Models.- 6.2.2 Models with Constant Conditional Correlations.- 6.2.3 Models with Random Coefficients.- 6.2.4 Model Based on a Spectral Decomposition.- 6.2.5 Factor ARCH Models.- 6.3 Estimation of Heteroscedastic Dynamic Models.- 6.3.1 Pseudo Maximum Likelihood Estimators.- 6.3.2 Asymptotic Properties of the Pseudo Maximum Likelihood Estimator.- 6.3.3 Model with Constant Conditional Correlations.- 6.3.4 Factor Models.- 7 Efficient Portfolios and Hedging Portfolios.- 7.1 Determination of an Efficient Portfolio.- 7.1.1 Securities and Portfolios.- 7.1.2 Mean Variance Criterion.- 7.1.3 Mean Variance Efficient Portfolios.- 7.2 Properties of the Set of Efficient Portfolios.- 7.2.1 The Set of Efficient Portfolios.- 7.2.2 Factors.- 7.3 Asymmetric Information and Aggregation.- 7.3.1 Incoherency of the Mean Variance Approach.- 7.3.2 Study of the Basic Portfolios.- 7.3.3 Aggregation.- 7.4 Hedging Portfolios.- 7.4.1 Determination of a Portfolio Mimicking a Series of Interest.- 7.4.2 A Model for the Call Seller Behavior.- 7.4.3 The Firm Behavior.- 7.5 Empirical Study of Performance Measures.- 7.5.1 Performances of a Set of Assets.- 7.5.2 Improving the Efficiency.- 7.5.3 Estimation of the Efficient Portfolio and its Performance in the Static Case.- 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.- 8.1.1 Linear Factor Representation.- 8.1.2 Representation with Endogenous Factors.- 8.1.3 Structure of the Conditional Moments.- 8.1.4 Cofactors.- 8.1.5 Characterization with the Matrix Defining the Endogenous Factors.- 8.2 Arbitrage Theory.- 8.2.1 Absence of Arbitrage Opportunities.- 8.2.2 Diversification and Pricing Model.- 8.2.3 Diversification and Risk Aversion.- 8.3 Efficiency Tests and Diversification.- 8.3.1 Ex-Ante Efficiency.- 8.3.2 Ex-Post Efficiency.- 8.4 Conditional and Historical Performance Measures.- 8.4.1 The Dynamics of a Model with Endogenous Factors.- 8.4.2 Tests for Ex-Ante Efficiency and Performances...- 8.5 Exercises.- 9 Equilibrium Models.- 9.1 Capital Asset Pricing Model.- 9.1.1 Description of the Model.- 9.1.2 Market Portfolio.- 9.1.3 The CAPM as a Factor Model.- 9.1.4 Spectral Decomposition of the Moments.- 9.1.5 Time Dependent Risk Aversion.- 9.2 Test of the CAPM.- 9.2.1 Some Difficulties.- 9.2.2 Testing Procedures in a Static Framework.- 9.2.3 Test for Efficiency of the Market Portfolio in a Dynamic Framework with Constant Betas.- 9.2.4 Tests in the General Case.- 9.3 Examples of Structural Models.- 9.3.1 A Model with Speculative Bubbles.- 9.3.2 The Consumption Based CAPM.