Written by leading market risk academic, Professor Carol Alexander, Practical Financial Econometrics forms part two of the Market Risk Analysis four volume set. It introduces the econometric techniques that are commonly applied to finance with a critical and selective exposition, emphasising the areas of econometrics, such as GARCH, cointegration and copulas that are required for resolving problems in market risk analysis. The book covers material for a one-semester graduate course in applied financial econometrics in a very pedagogical fashion as each time a concept is introduced an empirical example is given, and whenever possible this is illustrated with an Excel spreadsheet. All together, the Market Risk Analysis four volume set illustrates virtually every concept or formula with a practical, numerical example or a longer, empirical case study. Across all four volumes there are approximately 300 numerical and empirical examples, 400 graphs and figures and 30 case studies many of which are contained in interactive Excel spreadsheets available from the the accompanying CD-ROM. Empirical examples and case studies specific to this volume include: Factor analysis with orthogonal regressions and using principal component factors;Estimation of symmetric and asymmetric, normal and Student t GARCH and E-GARCH parameters;Normal, Student t, Gumbel, Clayton, normal mixture copula densities, and simulations from these copulas with application to VaR and portfolio optimization;Principal component analysis of yield curves with applications to portfolio immunization and asset/liability management;Simulation of normal mixture and Markov switching GARCH returns;Cointegration based index tracking and pairs trading, with error correction and impulse response modelling;Markov switching regression models (Eviews code);GARCH term structure forecasting with volatility targeting;Non-linear quantile regressions with applications to hedging.
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Written by leading market risk academic, Professor Carol Alexander, Practical Financial Econometrics forms part two of the Market Risk Analysis four volume set.
List of Figures xiii List of Tables xvii List of Examples xx Foreword xxii Preface to Volume II xxvi II. 1 Factor Models 1 II.1. 1 Introduction 1 II.1. 2 Single Factor Models 2 II.1.2. 1 Single Index Model 2 II.1.2. 2 Estimating Portfolio Characteristics using OLS 4 II.1.2. 3 Estimating Portfolio Risk using EWMA 6 II.1.2. 4 Relationship between Beta, Correlation and Relative Volatility 8 II.1.2. 5 Risk Decomposition in a Single Factor Model 10 II.1. 3 Multi-Factor Models 11 II.1.3. 1 Multi-factor Models of Asset or Portfolio Returns 11 II.1.3. 2 Style Attribution Analysis 13 II.1.3. 3 General Formulation of Multi-factor Model 16 II.1.3. 4 Multi-factor Models of International Portfolios 18 II.1. 4 Case Study: Estimation of Fundamental Factor Models 21 II.1.4. 1 Estimating Systematic Risk for a Portfolio of US Stocks 22 II.1.4. 2 Multicollinearity: A Problem with Fundamental Factor Models 23 II.1.4. 3 Estimating Fundamental Factor Models by Orthogonal Regression 25 II.1. 5 Analysis of Barra Model 27 II.1.5. 1 Risk Indices, Descriptors and Fundamental Betas 28 II.1.5. 2 Model Specification and Risk Decomposition 30 II.1. 6 Tracking Error and Active Risk 31 II.1.6. 1 Ex Post versus Ex Ante Measurement of Risk and Return 32 II.1.6. 2 Definition of Active Returns 32 II.1.6. 3 Definition of Active Weights 33 II.1.6. 4 Ex Post Tracking Error 33 II.1.6. 5 Ex Post Mean-Adjusted Tracking Error 36 II.1.6. 6 Ex Ante Tracking Error 39 II.1.6. 7 Ex Ante Mean-Adjusted Tracking Error 40 II.1.6. 8 Clarification of the Definition of Active Risk 42 II.1. 7 Summary and Conclusions 44 II. 2 Principal Component Analysis 47 II.2. 1 Introduction 47 II.2. 2 Review of Principal Component Analysis 48 II.2.2. 1 Definition of Principal Components 49 II 2 Principal Component Representation 49 II.2.2. 3 Frequently Asked Questions 50 II.2. 3 Case Study: PCA of UK Government Yield Curves 53 II.2.3. 1 Properties of UK Interest Rates 53 II.2.3. 2 Volatility and Correlation of UK Spot Rates 55 II.2.3. 3 PCA on UK Spot Rates Correlation Matrix 56 II.2.3. 4 Principal Component Representation 58 II.2.3. 5 PCA on UK Short Spot Rates Covariance Matrix 60 II.2. 4 Term Structure Factor Models 61 II.2.4. 1 Interest Rate Sensitive Portfolios 62 II.2.4. 2 Factor Models for Currency Forward Positions 66 II.2.4. 3 Factor Models for Commodity Futures Portfolios 70 II.2.4. 4 Application to Portfolio Immunization 71 II.2.4. 5 Application to Asset–Liability Management 72 II.2.4. 6 Application to Portfolio Risk Measurement 73 II.2.4. 7 Multiple Curve Factor Models 76 II.2. 5 Equity PCA Factor Models 80 II.2.5. 1 Model Structure 80 II.2.5. 2 Specific Risks and Dimension Reduction 81 II.2.5. 3 Case Study: PCA Factor Model for DJIA Portfolios 82 II.2. 6 Summary and Conclusions 86 II. 3 Classical Models of Volatility and Correlation 89 II.3. 1 Introduction 89 II.3. 2 Variance and Volatility 90 II.3.2. 1 Volatility and the Square-Root-of-Time Rule 90 II.3.3. 2 Constant Volatility Assumption 92 II.3.2. 3 Volatility when Returns are Autocorrelated 92 II.3.2. 4 Remarks about Volatility 93 II.3. 3 Covariance and Correlation 94 II.3.3. 1 Definition of Covariance and Correlation 94 II.3.3. 2 Correlation Pitfalls 95 II 3 Covariance Matrices 96 II.3.3. 4 Scaling Covariance Matrices 97 II.3. 4 Equally Weighted Averages 98 II.3.4. 1 Unconditional Variance and Volatility 99 II.3.4. 2 Unconditional Covariance and Correlation 102 II.3.4. 3 Forecasting with Equally Weighted Averages 103 II.3. 5 Precision of Equally Weighted Estimates 104 II.3.5. 1 Confidence Intervals for Variance and Volatility 104 II.3.5. 2 Standard Error of Variance Estimator 106 II.3.5. 3 Standard Error of Volatility Estimator 107 II.3.5. 4 Standard Error of Correlation Estimator 109 II.3. 6 Case Study: Volatility and Correlation of US Treasuries 109 II.3.6. 1 Choosing the Data 110 II.3.6. 2 Our Data 111 II.3.6. 3 Effect of Sample Period 112 II.3.6. 4 How to Calculate Changes in Interest Rates 113 II.3. 7 Equally Weighted Moving Averages 115 II.3.7. 1 Effect of Volatility Clusters 115 II.3.7. 2 Pitfalls of the Equally Weighted Moving Average Method 117 II.3.7. 3 Three Ways to Forecast Long Term Volatility 118 II.3. 8 Exponentially Weighted Moving Averages 120 II.3.8. 1 Statistical Methodology 120 II.3.8. 2 Interpretation of Lambda 121 II.3.8. 3 Properties of EWMA Estimators 122 II.3.8. 4 Forecasting with EWMA 123 II.3.8. 5 Standard Errors for EWMA Forecasts 124 II.3.8. 6 RiskMetrics TM Methodology 126 II.3.8. 7 Orthogonal EWMA versus RiskMetrics EWMA 128 II.3. 9 Summary and Conclusions 129 II. 4 Introduction to GARCH Models 131 II.4. 1 Introduction 131 II.4. 2 The Symmetric Normal GARCH Model 135 II.4.2. 1 Model Specification 135 II.4.2. 2 Parameter Estimation 137 II.4.2. 3 Volatility Estimates 141 II.4.2. 4 GARCH Volatility Forecasts 142 II.4.2. 5 Imposing Long Term Volatility 144 II.4.2. 6 Comparison of GARCH and EWMA Volatility Models 147 II.4. 3 Asymmetric GARCH Models 147 II.4.3. 1 A-garch 148 II.4.3. 2 Gjr-garch 150 II.4.3. 3 Exponential GARCH 151 II.4.3. 4 Analytic E-GARCH Volatility Term Structure Forecasts 154 II.4.3. 5 Volatility Feedback 156 II.4. 4 Non-Normal GARCH Models 157 II.4.4. 1 Student t GARCH Models 157 II.4.4. 2 Case Study: Comparison of GARCH Models for the Ftse 100 159 II.4.4. 3 Normal Mixture GARCH Models 161 II 4 Markov Switching GARCH 163 II.4. 5 GARCH Covariance Matrices 164 II.4.5. 1 Estimation of Multivariate GARCH Models 165 II.4.5. 2 Constant and Dynamic Conditional Correlation GARCH 166 II.4.5. 3 Factor GARCH 169 II.4. 6 Orthogonal GARCH 171 II.4.6. 1 Model Specification 171 II.4.6. 2 Case Study: A Comparison of RiskMetrics and O-GARCH 173 II.4.6. 3 Splicing Methods for Constructing Large Covariance Matrices 179 II.4. 7 Monte Carlo Simulation with GARCH Models 180 II.4.7. 1 Simulation with Volatility Clustering 180 II.4.7. 2 Simulation with Volatility Clustering Regimes 183 II.4.7. 3 Simulation with Correlation Clustering 185 II.4. 8 Applications of GARCH Models 188 II.4.8. 1 Option Pricing with GARCH Diffusions 188 II.4.8. 2 Pricing Path-Dependent European Options 189 II.4.8. 3 Value-at-Risk Measurement 192 II.4.8. 4 Estimation of Time Varying Sensitivities 193 II.4.8. 5 Portfolio Optimization 195 II.4. 9 Summary and Conclusions 197 II. 5 Time Series Models and Cointegration 201 II.5. 1 Introduction 201 II.5. 2 Stationary Processes 202 II.5.2. 1 Time Series Models 203 II.5.2. 2 Inversion and the Lag Operator 206 II.5.2. 3 Response to Shocks 206 II.5.2. 4 Estimation 208 II.5.2. 5 Prediction 210 II.5.2. 6 Multivariate Models for Stationary Processes 211 II.5. 3 Stochastic Trends 212 II.5.3. 1 Random Walks and Efficient Markets 212 II.5.3. 2 Integrated Processes and Stochastic Trends 213 II.5.3. 3 Deterministic Trends 214 II.5.3. 4 Unit Root Tests 215 II.5.3. 5 Unit Roots in Asset Prices 218 II.5.3. 6 Unit Roots in Interest Rates, Credit Spreads and Implied Volatility 220 II.5.3. 7 Reconciliation of Time Series and Continuous Time Models 223 II.5.3. 8 Unit Roots in Commodity Prices 224 II.5. 4 Long Term Equilibrium 225 II.5.4. 1 Cointegration and Correlation Compared 225 II.5.4. 2 Common Stochastic Trends 227 II.5.4. 3 Formal Definition of Cointegration 228 II.5.4. 4 Evidence of Cointegration in Financial Markets 229 II.5.4. 5 Estimation and Testing in Cointegrated Systems 231 II.5.4. 6 Application to Benchmark Tracking 239 II.5.4. 7 Case Study: Cointegration Index Tracking in the Dow Jones Index 240 II.5.5 Modelling Short Term Dynamics 243 II.5.5.1 Error Correction Models 243 II.5.5. 2 Granger Causality 246 II.5.5. 3 Case Study: Pairs Trading Volatility Index Futures 247 II.5. 6 Summary and Conclusions 250 II. 6 Introduction to Copulas 253 II.6. 1 Introduction 253 II.6. 2 Concordance Metrics 255 II.6.2. 1 Concordance 255 II.6.2. 2 Rank Correlations 256 II.6. 3 Copulas and Associated Theoretical Concepts 258 II.6.3. 1 Simulation of a Single Random Variable 258 II.6.3. 2 Definition of a Copula 259 II.6.3. 3 Conditional Copula Distributions and their Quantile Curves 263 II.6.3. 4 Tail Dependence 264 II.6.3. 5 Bounds for Dependence 265 II.6. 4 Examples of Copulas 266 II.6.4. 1 Normal or Gaussian Copulas 266 II.6.4. 2 Student t Copulas 268 II.6.4. 3 Normal Mixture Copulas 269 II.6.4. 4 Archimedean Copulas 271 II.6. 5 Conditional Copula Distributions and Quantile Curves 273 II.6.5. 1 Normal or Gaussian Copulas 273 II.6.5. 2 Student t Copulas 274 II.6.5. 3 Normal Mixture Copulas 275 II.6.5. 4 Archimedean Copulas 275 II.6.5. 5 Examples 276 II.6. 6 Calibrating Copulas 279 II.6.6. 1 Correspondence between Copulas and Rank Correlations 280 II.6.6. 2 Maximum Likelihood Estimation 281 II.6.6. 3 How to Choose the Best Copula 283 II.6. 7 Simulation with Copulas 285 II.6.7. 1 Using Conditional Copulas for Simulation 285 II.6.7. 2 Simulation from Elliptical Copulas 286 II.6.7. 3 Simulation with Normal and Student t Copulas 287 II.6.7. 4 Simulation from Archimedean Copulas 290 II.6. 8 Market Risk Applications 290 II.6.8. 1 Value-at-Risk Estimation 291 II.6.8. 2 Aggregation and Portfolio Diversification 292 II.6.8. 3 Using Copulas for Portfolio Optimization 295 II.6. 9 Summary and Conclusions 298 II. 7 Advanced Econometric Models 301 II.7. 1 Introduction 301 II.7. 2 Quantile Regression 303 II.7.2. 1 Review of Standard Regression 304 II.7.2. 2 What is Quantile Regression? 305 II.7.2. 3 Parameter Estimation in Quantile Regression 305 II.7.2. 4 Inference in Linear Quantile Regression 307 II.7.2. 5 Using Copulas for Non-linear Quantile Regression 307 II.7. 3 Case Studies on Quantile Regression 309 II.7.3. 1 Case Study 1: Quantile Regression of Vftse on FTSE 100 Index 309 II.7.3. 2 Case Study 2: Hedging with Copula Quantile Regression 314 II.7. 4 Other Non-Linear Regression Models 319 II.7.4. 1 Non-linear Least Squares 319 II.7.4. 2 Discrete Choice Models 321 II.7. 5 Markov Switching Models 325 II.7.5. 1 Testing for Structural Breaks 325 II.7.5. 2 Model Specification 327 II.7.5. 3 Financial Applications and Software 329 II.7. 6 Modelling Ultra High Frequency Data 330 II.7.6. 1 Data Sources and Filtering 330 II.7.6. 2 Modelling the Time between Trades 332 II.7.6. 3 Forecasting Volatility 334 II.7. 7 Summary and Conclusions 337 II. 8 Forecasting and Model Evaluation 341 II.8. 1 Introduction 341 II.8. 2 Returns Models 342 II.8.2. 1 Goodness of Fit 343 II.8.2. 2 Forecasting 347 II.8.2. 3 Simulating Critical Values for Test Statistics 348 II.8.2. 4 Specification Tests for Regime Switching Models 350 II.8. 3 Volatility Models 350 II.8.3. 1 Goodness of Fit of GARCH Models 351 II.8.3. 2 Forecasting with GARCH Volatility Models 352 II.8.3. 3 Moving Average Models 354 II.8. 4 Forecasting the Tails of a Distribution 356 II.8.4. 1 Confidence Intervals for Quantiles 356 II.8.4. 2 Coverage Tests 357 II.8.4. 3 Application of Coverage Tests to GARCH Models 360 II.8.4. 4 Forecasting Conditional Correlations 361 II.8. 5 Operational Evaluation 363 II.8.5. 1 General Backtesting Algorithm 363 II.8.5. 2 Alpha Models 365 II.8.5. 3 Portfolio Optimization 366 II.8.5. 4 Hedging with Futures 366 II.8.5. 5 Value-at-Risk Measurement 367 II.8.5. 6 Trading Implied Volatility 370 II.8.5. 7 Trading Realized Volatility 372 II.8.5. 8 Pricing and Hedging Options 373 II.8. 6 Summary and Conclusions 375 References 377 Index 387
Les mer
Written by leading market risk academic, Professor Carol Alexander, Practical Financial Econometrics forms part two of the Market Risk Analysis four volume set. It introduces the econometric techniques that are commonly applied to finance with a critical and selective exposition, emphasising the areas of econometrics, such as GARCH, cointegration and copulas that are required for resolving problems in market risk analysis. The book covers material for a one-semester graduate course in applied financial econometrics in a very pedagogical fashion as each time a concept is introduced an empirical example is given, and whenever possible this is illustrated with an Excel spreadsheet. All together, the Market Risk Analysis four volume set illustrates virtually every concept or formula with a practical, numerical example or a longer, empirical case study. Across all four volumes there are approximately 300 numerical and empirical examples, 400 graphs and figures and 30 case studies many of which are contained in interactive Excel spreadsheets available from the the accompanying CD-ROM . Empirical examples and case studies specific to this volume include: Factor analysis with orthogonal regressions and using principal component factors;Estimation of symmetric and asymmetric, normal and Student tGARCH and E-GARCH parameters;Normal, Student t, Gumbel, Clayton, normal mixture copula densities, and simulations from these copulas with application to VaR and portfolio optimization;Principal component analysis of yield curves with applications to portfolio immunization and asset/liability management;Simulation of normal mixture and Markov switching GARCH returns;Cointegration based index tracking and pairs trading, with error correction and impulse response modelling;Markov switching regression models (Eviews code);GARCH term structure forecasting with volatility targeting;Non-linear quantile regressions with applications to hedging.
Les mer

Produktdetaljer

ISBN
9780470998014
Publisert
2008-04-18
Utgiver
Vendor
John Wiley & Sons Inc
Vekt
907 gr
Høyde
249 mm
Bredde
175 mm
Dybde
31 mm
Aldersnivå
P, 06
Språk
Product language
Engelsk
Format
Product format
Annet format
Antall sider
432

Forfatter

Biographical note

Carol Alexander is a Professor of Risk Management at the ICMA Centre, University of Reading, and Chair of the Academic Advisory Council of the Professional Risk Manager’s International Association (PRMIA). She is the author of Market Models: A Guide to Financial Data Analysis(John Wiley & Sons Ltd, 2001) and has been editor and contributor of a very large number of books in finance and mathematics, including the multi-volume Professional Risk Manager's Handbook(McGraw-Hill, 2008 and PRMIA Publications). Carol has published nearly 100 academic journal articles, book chapters and books, the majority of which focus on financial risk management and mathematical finance. Professor Alexander is one of the world's leading authorities on market risk analysis. For further details, see www.icmacentre.rdg.ac.uk/alexander.