Market Models provides an authoritative and up-to-date treatment of the use of market data to develop models for financial analysis. Written by a leading figure in the field of financial data analysis, this book is the first of its kind to address the vital techniques required for model selection and development. Model developers are faced with many decisions, about the pricing, the data, the statistical methodology and the calibration and testing of the model prior to implementation. It is important to make the right choices and Carol Alexander's clear exposition provides valuable insights at every stage. 
In each of the 13 Chapters, Market Models presents real world illustrations to motivate theoretical developments. The accompanying CD contains spreadsheets with data and programs; this enables you to implement and adapt many of the examples. The pricing of options using normal mixture density functions to model returns; the use of Monte Carlo simulation to calculate the VaR of an options portfolio; modifying the covariance VaR to allow for fat-tailed P&L distributions; the calculation of implied, EWMA and 'historic' volatilities; GARCH volatility term structure forecasting; principal components analysis; and many more are all included. 
Carol Alexander brings many new insights to the pricing and hedging of options with her understanding of volatility and correlation, and the uncertainty which surrounds these key determinants of option portfolio risk. Modelling the market risk of portfolios is covered where the main focus is on a linear algebraic approach; the covariance matrix and principal component analysis are developed as key tools for the analysis of financial systems. The traditional time series econometric approach is also explained with coverage ranging from the application cointegration to long-short equity hedge funds, to high-frequency data prediction using neural networks and nearest neighbour algorithms. 
Throughout this text the emphasis is on understanding concepts and implementing solutions. It has been designed to be accessible to a very wide audience: the coverage is comprehensive and complete and the technical appendix makes the book largely self-contained. 
Market Models: A Guide to Financial Data Analysis is the ideal reference for all those involved in market risk measurement, quantitative trading and investment analysis.  

Contents:

Preface xv

Acknowledgements xvii

Part I: Volatility and Correlation Analysis

Chapter 1: Understanding Volatility and Correlation 3

1.1 The Statistical Nature of Volatility and Correlation 4

1.2 Volatility and Correlation in Financial Markets 9

1.3 Constant and Time-Varying Volatility Models 12

1.4 Constant and Time-Varying Correlation Models 14

1.5 Remarks on Implementing Volatility and Correlation Models 17

1.6 Summary 18

Chapter 2: Implied Volatility and Correlation 21

2.1 Understanding Implied Volatility* 22

2.1.1 Volatility in a Black-Scholes World 23

2.1.2 Call and Put Implied Volatilities 26

2.1.3 Differences between Implied and Statistical Volatilities 28

2.2 Features of Implied Volatility* 30

2.2.1 Smiles and Skews 30

2.2.2 Volatility Term Structures 31

2.2.3 Volatility Surfaces 32

2.3 The Relationship between Prices and Implied Volatility 34

2.3.1 Equity Prices and Volatility Regimes 34

2.3.2 Scenario Analysis of Prices and Implied Volatility 38

2.3.3 Implications for Delta Hedging 43

2.4 Implied Correlation 45

Chapter 3: Moving Average Models 49

3.1 Historic Volatility and Correlation* 50

3.1.1 Definition and Application 50

3.1.2 Historic Volatility in Financial Markets 52

3.1.3 Historic Correlation in Energy Markets 54

3.1.4 When and How Should Historic Estimates Be Used? 56

3.2 Exponentially Weighted Moving Averages* 57

3.3 Constant Volatility and the Square Root of Time Rule 61

Chapter 4: GARCH Models 63

4.1 Introduction to Generalized Autoregressive Conditional Heteroscedasticity 65

4.1.1 Volatility Clustering 65

4.1.2 The Leverage Effect 68

4.1.3 The Conditional Mean and Conditional Variance Equations 69

4.2 A Survey of Univariate GARCH Models 70

4.2.1 ARCH 71

4.2.2 Symmetric GARCH* 72

4.2.3 Integrated GARCH and the Components Model 75

4.2.4 Asymmetric GARCH* 79

4.2.5 GARCH Models for High-Frequency Data 82

4.3 Specification and Estimation of GARCH Models 84

4.3.1 Choice of Data, Stability of GARCH Parameters

and Long-Term Volatility 84

4.3.2 Parameter Estimation Algorithms 94

4.3.3 Estimation Problems 96

4.3.4 Choosing the Best GARCH Model 96

4.4 Applications of GARCH Models 97

4.4.1 GARCH Volatility Term Structures* 98

4.4.2 Option Pricing and Hedging 103

4.4.3 Smile Fitting 106

4.5 Multivariate GARCH 107

4.5.1 Time-Varying Correlation 108

4.5.2 Multivariate GARCH Parameterizations 112

4.5.3 Time-Varying Co variance Matrices Based on

Univariate GARCH Models 114

Chapter 5: Forecasting Volatility and Correlation 117

5.1 Evaluating the Accuracy of Point Forecasts 119

5.1.1 Statistical Criteria 121

5.1.2 Operational Criteria 124

5.2 Confidence Intervals for Volatility Forecasts 126

5.2.1 Moving Average Models 126

5.2.2 GARCH Models 128

5.2.3 Confidence Intervals for Combined Forecasts 128

5.3 Consequences of Uncertainty in Volatility and Correlation 135

5.3.1 Adjustment in Mark-to-Model Value of an Option* 135

5.3.2 Uncertainty in Dynamically Hedged Portfolios 138

Part II: Modelling the Market Risk of Portfolios

Chapter 6: Principal Component Analysis 143

6.1 Mathematical Background 145

6.2 Application to Term Structures* 147

6.2.1 The Trend, Tilt and Convexity Components of a

Single Yield Curve 147

6.2.2 Modelling Multiple Yield Curves with PCA 149

6.2.3 Term Structures of Futures Prices 153

6.3 Modelling Volatility Smiles and Skews 154

6.3.1 PCA of Deviations from ATM Volatility 157

6.3.2 The Dynamics of Fixed Strike Volatilities in

Different Market Regimes 159

6.3.3 Parameterization of the Volatility Surface and

Quantification of da/dS 167

6.3.4 Summary 170

6.4 Overcoming Data Problems Using PCA 171

6.4.1 Multicollinearity 172

6.4.2 Missing Data 175

Chapter 7: Covariance Matrices 179

7.1 Applications of Covariance Matrices in Risk Management 180

7.1.1 The Variance of a Linear Portfolio 180

7.1.2 Simulating Correlated Risk Factor Movements

in Derivatives Portfolios 182

7.1.3 The Need for Positive Semi-definite Covariance Matrices* 183

7.1.4 Stress Testing Portfolios Using the Covariance Matrix* 184

7.2 Applications of Covariance Matrices in Investment Analysis 186

7.2.1 Minimum Variance Portfolios 187

7.2.2 The Relationship between Risk and Return 189

7.2.3 Capital Allocation and Risk-Adjusted Performance

Measures 193

7.2.4 Modelling Attitudes to Risk 194

7.2.5 Efficient Portfolios in Practice 198

7.3 The RiskMetrics Data 201

7.4 Orthogonal Methods for Generating Covariance Matrices 204

7.4.1 Using PCA to Construct Covariance Matrices 205

7.4.2 Orthogonal EWMA 206

7.4.3 Orthogonal GARCH 210

7.4.4 'Splicing' Methods for Obtaining Large Covariance Matrices 221

7.4.5 Summary 227

Chapter 8: Risk Measurement in Factor Models 229

8.1 Decomposing Risk in Factor Models 230

8.1.1 The Capital Asset Pricing Model 230

8.1.2 Multi-factor Fundamental Models 233

8.1.3 Statistical Factor Models 235

8.2 Classical Risk Measurement Techniques* 236

8.2.1 The Different Perspectives of Risk Managers and

Asset Managers 236

8.2.2 Methods Relevant for Constant Parameter Assumptions 237

8.2.3 Methods Relevant for Time-Varying Parameter

Assumptions 238

8.2.4 Index Stripping 238

8.3 Bayesian Methods for Estimating Factor Sensitivities 239

8.3.1 Bayes' Rule 240

8.3.2 Bayesian Estimation of Factor Models 242

8.3.3 Confidence in Beliefs and the Effect on Bayesian Estimates 245

8.4 Remarks on Factor Model Specification Procedures 246

Chapter 9: Value-at-Risk 249

9.1 Controlling the Risk in Financial Markets 250

9.1.1 The 1988 Basel Accord and the 1996 Amendment 251

9.1.2 Internal Models for Calculating Market Risk Capital Requirements 252

9.1.3 Basel 2 Proposals 255

9.2 Advantages and Limitations of Value-at-Risk 255

9.2.1 Comparison with Traditional Risk Measures 256

9.2.2 VaR-Based Trading Limits 257

9.2.3 Alternatives to VaR 257

9.3 Covariance VaR Models* 260

9.3.1 Basic Assumptions 260

9.3.2 Simple Cash Portfolios 261

9.3.3 Covariance VaR with Factor Models 262

9.3.4 Covariance VaR with Cash-Flow Maps 263

9.3.5 Aggregation 266

9.3.6 Advantages and Limitations 266

9.4 Simulation VaR Models* 267

9.4.1 Historical Simulation 268

9.4.2 Monte Carlo Simulation 270

9.4.3 Delta-Gamma Approximations 273

9.5 Model Validation 275

9.5.1 Backtesting Methodology and Regulatory

Classification 275

9.5.2 Sensitivity Analysis and Model Comparison 277

9.6 Scenario Analysis and Stress Testing* 278

9.6.1 Scenario Analysis 279

9.6.2 Probabilistic Scenario Analysis 280

9.6.3 Stress-Testing Portfolios 281

Chapter 10: Modelling Non-normal Returns 285

10.1 Testing for Non-normality in Returns Distributions* 286

10.1.1 Skewness and Excess Kurtosis 286

10.1.2 QQ Plots 288

10.2 Non-normal Distributions 290

10.2.1 Extreme Value Distributions 290

10.2.2 Hyperbolic Distributions 296

10.2.3 Normal Mixture Distributions* 297

10.3 Applications of Normal-Mixture Distributions* 301

10.3.1 Covariance VaR Measures 302

10.3.2 Term Structure Forecasts of Excess Kurtosis 303

10.3.3 Applications of Normal Mixtures to Option

Pricing and Hedging 305

Part III: Statistical Models for Financial Markets

Chapter 11: Time Series Models 315

11.1 Basic Properties of Time Series 316

11.1.1 Time Series Operators 316

11.1.2 Stationary Processes and Mean-Reversion 317

11.1.3 Integrated Processes and Random Walks 320

11.1.4 Detrending Financial Time Series Data 322

11.1.5 Unit Root Tests* 324

11.1.6 Testing for the Trend in Financial Markets 328

11.2 Univariate Time Series Models 329

11.2.1 AR Models 329

11.2.2 MA Models 331

11.2.3 ARMA Models 332

11.3 Model Identification* 333

11.3.1 Correlograms 333

11.3.2 Autocorrelation Tests 335

11.3.3 Testing Down 337

11.3.4 Forecasting with ARMA Models 338

11.4 Multivariate Time Series 340

11.4.1 Vector Autoregressions 340

11.4.2 Testing for Joint Covariance Stationarity 341

11.4.3 Granger Causality 344

Chapter 12: Cointegration 347

12.1 Introducing Cointegration 348

12.1.1 Cointegration and Correlation 349

12.1.2 Common Trends and Long-Run Equilibria 350

12.2 Testing for Cointegration* 353

12.2.1 The Engle-Granger Methodology 354

12.2.2 The Johansen Methodology 357

12.3 Error Correction and Causality 361

12.4 Cointegration in Financial Markets 366

12.4.1 Foreign Exchange 366

12.4.2 Spot and Futures 367

12.4.3 Commodities 367

12.4.4 Spread Options 367

12.4.5 Term Structures 368

12.4.6 Market Integration 368

12.5 Applications of Cointegration to Investment Analysis 369 12.5.1 Selection and Allocation 370

12.5.2 Constrained Allocations 371

12.5.3 Parameter Selection 372

12.5.4 Long-Short Strategies 375

12.5.5 Backtesting 375 12.6 Common Features 381

12.6.1 Common Autocorrelation 385

12.6.2 Common Volatility 386

Chapter 13: Forecasting High-Frequency Data 389

13.1 High-Frequency Data 390

13.1.1 Data and Information Sources 390

13.1.2 Data Filters 391

13.1.3 Autocorrelation Properties 391

13.1.4 Parametric Models of High-Frequency Data 393

13.2 Neural Networks 395

13.2.1 Architecture 396

13.2.2 Data Processing 397

13.2.3 Backpropagation 398

13.2.4 Performance Measurement 399

13.2.5 Integration 400

13.3 Price Prediction Models Based on Chaotic Dynamics 401

13.3.1 Testing for Chaos 401

13.3.2 Nearest Neighbour Algorithms 403

13.3.3 Multivariate Embedding Methods 405

Technical Appendices 409

A.l Linear Regression* 409

A. 1.1 The Simple Linear Model 410

A. 1.2 Multivariate Models 412

A. 1.3 Properties of OLS Estimators 414

A. 1.4 Estimating the Covariance Matrix of the OLS Estimators 419

A.2 Statistical Inference 421

A.2.1 Hypothesis Testing and Confidence Intervals 421

A.2.2 /-tests 424

A.2.3 F-test 426

A.2.4 The Analysis of Variance 427

A.2.5 Wald, Lagrange Multiplier and Likelihood Ratio Tests 428

A.3 Residual Analysis 429

A.3.1 Autocorrelation 430

A.3.2 Unconditional Heteroscedasticity 432

A.3.3 Generalized Least Squares 433

A.4 Data Problems 436

A.4.1 Multicollinearity 436

A.4.2 Data Errors 437

A.4.3 Missing Data 439

A.4.4 Dummy Variables 440

А. 5 Prediction 443

А.5.1 Point Predictions and Confidence Intervals 443

A.5.2 Backtesting 444

A.5.3 Statistical and Operational Evaluation Methods 445

A.6 Maximum Likelihood Methods 447

A.6.1 The Likelihood Function, MLE and LR Tests 447

A.6.2 Properties of Maximum Likelihood Estimators 449

A.6.3 MLEs for a Normal Density Function 449

A.6.4 MLEs for Non-normal Density Functions 451

References 453

Tables 467

Index 475