A Practitioners Guide to Financial Data Analysis*
Part 1: Volatility and Correlation Analysis
Chapter 1: Understanding Volatility and Correlation
1.1 The Statistical Nature of Volatility and Correlation
2.1 Understanding Implied Volatility*
3.1 Historic Volatility and Correlation*
4.1 The Nature of Generalized Autoregressive Conditional Heteroscedasticity
5.1 Evaluating the Accuracy of Point Forecasts
Chapter 6: Principal Component Analysis
6.1 Mathematical Background
Chapter 7: Covariance Matrices
7.1 Applications of Covariance Matrices in Risk Management*
8.1 Decomposing Risk in Factor Models*
9.1 Controlling the Risk in Financial Markets
10.1 Testing For Non-Normality in Returns Distributions
Chapter 11: Time Series Models
11.1 Basic Properties of Time Series
12.1 Introducing Cointegration
13.1 High Frequency Data
A.1 Linear Regression
1.2 Volatility and Correlation in Financial markets
1.3 Constant and Time Varying Volatility Models
1.4 Constant and Time Varying Correlation Models
1.5 Remarks on the Implementation of Volatility and Correlation Models
1.6 Summary
Chapter 2: Implied Volatility and Correlation
2.1.1 Volatility in a Black-Scholes World
2.1.2 Call and Put Implied Volatilities
2.1.3 Differences Between Implied and Statistical Volatilities
2.2 Features of Implied Volatility*
2.2.1 Smiles and Skews
2.2.2 Volatility Term Structures
2.2.3 Volatility Surfaces
2.3 The Relationship between Price and Implied Volatility
2.3.1 Equity Prices and Volatility Regimes
2.3.2 Scenario Analysis of Prices and Implied Volatilities
2.3.3 Implications for Delta-Hedging
2.4 Implied Correlation
Chapter 3: Moving Average Models
3.1.1 Definition
3.1.2 Historic Volatility in Financial Markets
3.1.3 Historic Correlation in Energy Markets
3.1.4 When and How should Historic Estimates be Used?
3.2 Exponentially Weighted Moving Averages*
3.3 Constant Volatility and The Square Root of Time Rule
Chapter 4: GARCH Models
4.1.1 Volatility Clustering
4.1.2 The Leverage Effect
4.1.3 The Conditional Mean and Conditional Variance Equations
4.2 A Survey of Univariate GARCH Models*
4.2.1 ARCH
4.2.2 Vanilla GARCH
4.2.3 Integrated and Components GARCH
4.2.4 Asymmetric GARCH Models
4.2.5 GARCH Models for High Frequency Data
4.3 Specification and Estimation of GARCH Models
4.3.1 Choice of Data, Stability of GARCH Parameters and Long-Term Volatility
4.3.2 Parameter Estimation Algorithms
4.3.3 Estimation Problems
4.3.4 Choosing the Best GARCH Model
4.4 Applications of GARCH Models
4.4.1 GARCH Volatility Term Structures*
4.4.2 Option Pricing and Hedging
4.4.3 Smile Fitting
4.5 Multivariate GARCH
4.5.1 Time-Varying Correlation
4.5.2 Multivariate GARCH Parameterizations
4.5.3 Time-Varying Covariance Matrices Based on Univarite GARCH Models
Chapter 5: Forecasting Volatility and Correlation
5.1.1 Statistical Criteria
5.1.2 Operational Criteria
5.2 Confidence Intervals for Volatility Forecasts
5.2.1 Moving Average Models
5.2.2 GARCH Models
5.2.3 Confidence Intervals for Combined Forecasts
5.3 Consequences of Uncertainty in Volatility and Correlation
5.3.1 Adjustment in Mark-to-Model Value of an Option*
5.3.2 Uncertainty in Dynamically Hedged Portfolios
Part 2: Modelling the Market Risk of Portfolios
6.2 Applications to Term Structures*
6.2.1 The Trend, Tilt and Convexity Components of a Single Yield Curve
6.2.2 Modelling Multiple Yield Curves with PCA
6.2.3 Term Structures of Futures Prices
6.3 Modelling Volatility Smiles and Skews
6.3.1 PCA of Deviations from ATM Volatility
6.3.2 The Dynamics of Implied Volatilities in Different Market Regimes
6.3.3 Parameterization of the Volatility Surface and Quantification of s/S
6.3.4 Summary
6.4 Overcoming Data Problems using PCA
6.4.1 Multicollinearity
6.4.2 Missing Data
7.1.1 The Variance of a Linear Portfolio
7.1.2 Simulating Correlated Risk Factor Movements for Derivatives Portfolios
7.1.3 The Need for Positive Semi-Definite Covariance Matrices
7.1.4 Stress Testing Portfolios using the Covariance Matrix
7.2 Applications of Covariance Matrices in Investment Analysis
7.2.1 Minimum Variance Portfolios
7.2.2 The Relationship Between Risk and Return
7.2.3 Capital Allocation and Risk Adjusted Performance Measures
7.2.4 Modelling Attitude to Risk
7.2.5 Efficient Portfolios in Practice
7.3 The RiskMetrics Data
7.4 Orthogonal Methods for Generating Covariance Matrices
7.4.1 Using PCA to Construct Covariance Matrices
7.4.2 Orthogonal EWMA
7.4.3 Orthogonal GARCH
7.4.4 Splicing Methods for Generating Large Covariance Matrices
7.4.5 Summary
Chapter 8: Risk Measurement in Factor Models
8.1.1 The CAPM Model
8.1.2 Multi-Factor Fundamental Models
8.1.3 Statistical Factor Models
8.2 Classical Risk Measurement Techniques*
8.2.1 The Different Perspectives of Risk Managers and Asset Managers
8.2.2 Methods Relevant for Constant Parameter Assumptions
8.2.3 Methods Relevant for Time-Varying Parameter Assumptions
8.2.4 Index Stripping
8.3 Bayesian Methods for Estimating Factor Sensitivities
8.3.1 Bayes' Rule
8.3.2 Bayesian Estimation of Factor Models
8.3.3 Confidence in Beliefs and the Effect on Bayesian Estimates
8.4 Concluding Remarks on Factor Model Specification Procedures
Chapter 9: Value-At-Risk
9.1.1 The 1988 Basle Accord and the 1996 Amendment
9.1.2 Internal Models for Calculating Market Risk Capital Requirements
9.1.3 Basle 2 Proposals
9.2 Advantages and Limitations of Value-at-Risk
9.2.1 Comparison with Traditional Risk Measures
9.2.2 VaR Based Trading Limits
9.2.3 Alternatives to VaR
9.3 Covariance VaR Models*
9.3.1 Basic Assumptions
9.3.2 Simple Equity Portfolios
9.3.3 Covariance VaR with Factor Models
9.3.4 Covariance VaR of Cash-Flows
9.3.5 Aggregation
9.3.6 Advantages and Limitations
9.4 Simulation VaR Models*
9.4.1 Historical Simulation
9.4.2 Monte Carlo Simulation
9.4.3 Delta-Gamma Approximations
9.5 Model Validation
9.5.1 Backtesting Methodology and Regulatory Classification
9.5.2 Sensitivity Analysis and Model Comparison
9.6 Scenario Analysis and Stress Testing*
9.6.1 Scenario Analysis
9.6.2 Probabilistic Scenario Analysis
9.6.3 Stress Testing Portfolios
Chapter 10: Modelling Non-Normal Returns
10.1.1 Skewness and Excess Kurtosis
10.1.2 QQ Plots
10.2 Non-Normal Distributions
10.2.1 Extreme Value Distributions
10.2.2 Hyperbolic Distributions
10.2.3 Normal Mixture Distributions
10.3 Applications of Normal Mixture Distributions*
10.3.1 Covariance VaR Measures
10.3.2 Term Structure Forecasts of Excess Kurtosis
10.3.3 Option Pricing and Hedging with Leptokurtic Returns
Part 3: Statistical Models for Financial Markets
11.1.1 Time Series Operators
11.1.2 Stationary Processes and Mean-Reversion
11.1.3 Integrated Processes and Random Walks
11.1.4 Detrending Financial Time Series
11.1.5 Unit Root Tests*
11.1.6 Testing for the Trend in Financial Markets
11.2 Univariate Models for Stationary Time Series
11.2.1 AR Models
11.2.2 MA Models
11.2.3 ARMA Models
11.3 Model Identification and Forecasting Applications*
11.3.1 Correlograms
11.3.2 Autocorrelation Tests
11.3.3 Testing Down
11.3.4 Forecasting with ARMA Models
11.4 Multivariate Time Series*
11.4.1 Vector Autoregressive Models
11.4.2 Testing for Joint Covariance Stationarity
11.4.3 Granger Causality
Chapter 12: Cointegration
12.1.1 Cointegration vs Correlation
12.1.2 Common Trends and Long-Run Equilibria
12.2 Testing for Cointegration*
12.2.1 The Engle-Granger Methodology
12.2.2 The Johansen Methodology
12.3 Error Correction and Causality
12.4 Cointegration in Financial Markets
12.4.1 Foreign Exchange
12.4.2 Spot and Futures
12.4.3 Commodities
12.4.4 Spread Options
12.4.5 Term Structures
12.4.6 Market Integration
12.5 Applications of Cointegration to Investment Analysis
12.5.1 Selection and Allocation
12.5.2 Constrained Allocations
12.5.3 Parameter Selection
12.5.4 Long-Short Strategies
12.5.5 Back Testing
12.6 Common Features
12.5.1 Common Autocorrelation
12.5.2 Common Volatility
Chapter 13: Forecasting High-Frequency Data
13.1.1 Data and Information Sources
13.1.2 Data Filters
13.1.3 Autocorrelation Properties
13.1.4 Parametric Models of High Frequency Data
13.2 Neural Networks
13.2.1 Architecture
13.2.2 Data Processing
13.2.3 Backpropagation
13.2.4 Performance Measurement
13.2.5 Integration
13.3 Price Prediction Models Based on Chaotic Dynamics
13.3.1 Testing for Chaos
13.3.2 Embedding Methods
13.3.3 Nearest Neighbour Algorithms
13.3.4 Multivariate Embedding Methods
Technical Appendix
A.1.1 The Simple Linear Model
A.1.2 Multivariate Models
A.1.3 Properties of OLS Estimators
A.1.4 Estimating the Covariance Matrix of the OLS Estimators
A.2 Statistical Inference
A.2.1 Hypothesis Testing and Confidence Intervals
A.2.2 t-tests
A.2.3 F-test
A.2.4 The Analysis of Variance
A.2.5 Wald, Lagrange Multiplier and Likelihood Ratio Tests
A.3 Residual Analysis
A.3.1 Testing for Autocorrelation
A.3.2 Testing for Heteroscedasticity
A.3.3 Generalised Least Squares
A.4 Data Problems
A.4.1 Multicollinearity
A.4.2 Data Errors
A.4.3 Missing Data
A.4.4 Dummy Variables
A.5 Prediction
A.5.1 Point Predictions and Confidence Intervals
A.5.2 Back Testing
A.5.3 Statistical and Operational Evaluation Methods
A.6 Maximum Likelihood Methods
A.6.1 The Likelihood Function, MLE and LR Tests
A.6.2 Properties of Maximum Likelihood Estimators
A.6.3 MLEs for a Normal Density Function
A.6.4 MLEs for Non-normal Density Functions
