Market Models

Contents

Chapter 1: Linear Models.

• 1.1 Introduction.
• 1.1.1 The Simple Linear Model.
• 1.1.2 The Capital Asset Pricing Model.
• 1.1.3 Risk Attribution in the Capital Asset Pricing Model.
• 1.2 Multivariate Models.
• 1.2.1 Ordinary Least Squares.
• 1.2.2 The Arbitrage Pricing Model.
• 1.2.3 Estimating Factor Sensitivities in the Arbitrage Pricing Model.
• 1.2.4 Using Multifactor Models to Analyse Portfolio Risk.
• 1.2.5 Benchmarking and Index Tracking.
• 1.3 Properties of Estimators.
• 1.3.1 Unbiasedness, Efficiency and Consistency.
• 1.3.2. Properties of OLS Estimators with Non-Stochastic Regressors.
• 1.3.3 Properties of OLS with Stochastic Regressors.
• 1.3.4 Estimating the Covariance Matrix of the OLS Estimators.
• 1.3.5 When are OLS Estimators Normally Distributed?
• 1.4 Statistical Inference.
• 1.4.1 Hypothesis Testing and Confidence Intervals.
• 1.4.2 t-tests.
• 1.4.3 F-tests.
• 1.4.4 The Analysis of Variance.
• 1.4.5 Wald, Lagrange Multiplier and Likelihood Ratio Tests.
• 1.5 Model Specification.
• 1.5.1 Autocorrelation.
• 1.5.2 Unconditional Heteroscedasticity.
• 1.5.3 Generalised Least Squares.
• 1.5.4 Testing Down.
• 1.5.5 A Remark on Model Specification.
• 1.6 Data Problems.
• 1.6.1 Multicollinearity.
• 1.6.2 Errors in Measurement.
• 1.6.3 Missing Data.
• 1.6.4 Dummy Variables.
• 1.7 Principal Components Analysis.
• 1.7.1 Definition and General Applications.
• 1.7.2 Application of PCA to Yield Curves.
• 1.7.3 Orthogonal Factor Models.
• 1.7.4 Using PCA to Generate Covariance Matrices.
• 1.8 Likelihood Methods and Bayesian Inference.
• 1.8.1 The Likelihood Function, MLE and LR Tests.
• 1.8.2 Propertiesof Maximum Likelihood Estimators.
• 1.8.3 Likelihood Function and MLE for a Normal Density Function.
• 1.8.4 Applications of Maximum Likelihood to Financial Markets.
• 1.8.5 Introducing Bayesian Estimation.
• 1.8.6 Bayesian Estimation of Factor Models.
• 1.9 Forecasting and Model Validation.
• 1.9.1 Point Predictions and Confidence Intervals.
• 1.9.2 Post-sample Predictive Testing and Back Testing.
• 1.9.3 Statistical Evaluation Methods.
• 1.9.4 Operational Evaluation Methods.
• 1.10 Mean-Variance Analysis.
• 1.10.1 Minimum Variance Portfolios.
• 1.10.2 Utility Theory.
• 1.10.3 Efficient Portfolios with a Risk Free Asset.
• 1.10.4 Efficient Portfolios in Practice.

• 2.1 The Nature of Volatility and Correlation.
• 2.1.1 Statistical Definitions.
• 2.1.2 Implied Volatility.
• 2.1.3 Implied Correlation.
• 2.1.4 Conditional and Unconditional Distributions.
• 2.2 Weighted Average Estimates of Volatility and Correlation.
• 2.2.1 Equally Weighted Moving Averages.
• 2.2.2 Exponentially Weighted Moving Averages.
• 2.2.3 The Square Root of Time Rule.
• 2.2.4 The RiskMetrics Data.
• 2.2.5 An Alternative to RiskMetrics.
• 2.3 Generalized Autoregressive Conditional Heteroscedasticity.
• 2.3.1 The Conditional Mean and Conditional Variance Equations.
• 2.3.2 A Survey of Univariate GARCH Models.
• 2.3.3 Getting the Right Data for GARCH Modelling.
• 2.3.4 GARCH Parameter Estimation and Model Specification.
• 2.3.5 GARCH Volatility Forecasting.
• 2.3.6 Option Pricing and Hedging with Univariate GARCH.
• 2.3.7 GARCH Correlation and Time Varying Betas.
• 2.3.8 A Survey of Multivariate GARCH Models.
• 2.3.9 Comparison of Results from Different Multivariate GARCH Models.
• 2.4 Forecasting Volatility and Correlation.
• 2.4.1 Combining Volatility Forecasts.
• 2.4.2 Methods for Evaluating the Accuracy of Point Forecasts.
• 2.4.3 Confidence Intervals.
• 2.4.4 Generating P&L Distributions Due to Uncertain Volatility.
• 2.4.5 A Bayesian Approach to Volatility Forecasting.

• 3.1 Stationary and Integrated Processes.
• 3.1.1 Introduction.
• 3.1.2 ARMA Models.
• 3.1.3 Unit Root Tests.
• 3.1.4 Time Series Properties of Financial Markets.
• 3.2 Cointegration.
• 3.2.1 Introduction.
• 3.2.2 Cointegration Tests.
• 3.2.3 Error Correction and Causality.
• 3.2.4 Cointegration and Market Efficiency.
• 3.3 Applications of Cointegration to Financial Markets.
• 3.3.1 Yield Curves.
• 3.3.2 Spot and Futures Markets.
• 3.3.3 Energy Markets.
• 3.3.4 Equity Markets.
• 3.3.5 Market Integration.
• 3.4 Modelling High Frequency Data.
• 3.4.1 Properties of High Frequency Financial Data.
• 3.4.2 Modelling Non-Normal Distributions of High Frequency Returns.
• 3.4.3 Chaos in Financial Markets.
• 3.4.4 Neural Networks and Non-Linear Prediction Algorithms.

• 4.1 The Regulatory Environment.
• 4.1.1 Recommendations for Internal Models of Market Risk Capital.
• 4.1.2 Comparison with Capital Charges based on Standardised Rules.
• 4.1.3 Back Testing and Model Classification.
• 4.1.4 Stress Testing Portfolios.
• 4.2 Measuring Risk.
• 4.2.1 Advantages and Limitations of VaR.
• 4.2.2 Coherent Risk Measures.
• 4.2.3 Measuring Downside Risk.
• 4.3 The Covariance Method.
• 4.3.1 Linear Portfolios.
• 4.3.2 Covariance VaR of Equity Portfolios.
• 4.3.3 Covariance VaR of Commodities and Cash-Flows.
• 4.3.4 Advantages and Limitations.
• 4.4 Historical Simulation.
• 4.4.1 Outline of Method.
• 4.4.2 Comparison with Covariance VaR.
• 4.4.3 Modifications: Exponential Weighting and Cholesky Transformations.
• 4.4.4 Advantages and Limitations.
• 4.5 Monte Carlo Methods.
• 4.5.1 Risk Factors in Options Portfolios.
• 4.5.2 Method Outlined.
• 4.5.3 Modifications: Advanced Sampling and Portfolio Value Approximations.
• 4.5.4 Advantages and Limitations.
• 4.6 Scenario Analysis.
• 4.6.1 The Scenario Library.
• 4.6.2 Grid Search for Worst Case Loss.
• 4.6.3 Scenario Analysis using Principal Components.
• 4.6.4 Stress Testing.