Normal view MARC view

Market risk analysis

Author: Alexander, Carol Publisher: Wiley, 2008.Language: EnglishDescription: 25 cm. includes CD-ROM / DVDISBN: 9780470998007 ; 978-0-470-998014Type of document: BookNote: CD available inside each back coverBibliography/Index: Includes indexContents Note: Vol. 1 "Quantitative methods in finance", 290 p. ; Vol. 2 "Practical financial econometrics", 396 p. ; Vol. 3 "Pricing, hedging and trading financial instruments", 386 p. ; Vol. 4 "Value-at-risk models", 449 p.
Tags: No tags from this library for this title. Log in to add tags.
Item type Current location Collection Call number Status Date due Barcode Item holds
Book Europe Campus
Main Collection
Print HG6024.3 .A54 2008 Vol. 1
(Browse shelf)
001241822
Available 001241822
Book Europe Campus
Main Collection
Print HG6024.3 .A54 2008 Vol. 2
(Browse shelf)
001241846
Available 001241846
Book Europe Campus
Main Collection
Print HG6024.3 .A54 2008 Vol. 3
(Browse shelf)
001241839
Available 001241839
Book Europe Campus
Main Collection
Print HG6024.3 .A54 2008 Vol. 4
(Browse shelf)
001246537
Available 001246537
Total holds: 0

CD available inside each back cover

Includes index

Vol. 1 "Quantitative methods in finance", 290 p. ; Vol. 2 "Practical financial econometrics", 396 p. ; Vol. 3 "Pricing, hedging and trading financial instruments", 386 p. ; Vol. 4 "Value-at-risk models", 449 p.

Digitized

Market Risk Analysis Volume I Quantitative Methods in Finance Contents List of Figures List of Tables List of Examples Foreword Preface to Volume I I.1 Basic Calculus for Finance I.1.1 Introduction I.1.2 Functions and Graphs, Equations and Roots I.1.2.1 Linear and Quadratic Functions I.1.2.2 Continuous and Differentiable Real-Valued Functions I.1.2.3 Inverse Functions I.1.2.4 The Exponential Function I.1.2.5 The Natural Logarithm I.1.3 Differentiation and Integration I.1.3.1 Definitions I.1.3.2 Rules for Differentiation I.1.3.3 Monotonic, Concave and Convex Functions I.1.3.4 Stationary Points and Optimization I.1.3.5 Integration I.1.4 Analysis of Financial Returns I.1.4.1 Discrete and Continuous Time Notation I.1.4.2 Portfolio Holdings and Portfolio Weights I.1.4.3 Profit and Loss I.1.4.4 Percentage and Log Returns I.1.4.5 Geometric Brownian Motion I.1.4.6 Discrete and Continuous Compounding in Discrete Time I.1.4.7 Period Log Returns in Discrete Time I.1.4.8 Return on a Linear Portfolio I.1.4.9 Sources of Returns I.1.5 Functions of Several Variables I.1.5.1 Partial Derivatives: Function of Two Variables I.1.5.2 Partial Derivatives: Function of Several Variables xiii xvi xvii xix xxiii 1 1 3 4 5 6 7 9 10 10 11 13 14 15 16 16 17 19 19 21 22 23 25 25 26 27 27 I.1.5.3 Stationary Points I.1.5.4 Optimization I.1.5.5 Total Derivatives I.1.6 Taylor Expansion I.1.6.1 Definition and Examples I.1.6.2 Risk Factors and their Sensitivities I.1.6.3 Some Financial Applications of Taylor Expansion I.1.6.4 Multivariate Taylor Expansion I.1.7 Summary and Conclusions 28 29 31 31 32 33 33 34 35 I.2 Essential Linear Algebra for Finance I.2.1 Introduction I.2.2 Matrix Algebra and its Mathematical Applications I.2.2.1 Basic Terminology I.2.2.2 Laws of Matrix Algebra I.2.2.3 Singular Matrices I.2.2.4 Determinants I.2.2.5 Matrix Inversion I.2.2.6 Solution of Simultaneous Linear Equations I.2.2.7 Quadratic Forms I.2.2.8 Definite Matrices I.2.3 Eigenvectors and Eigenvalues I.2.3.1 Matrices as Linear Transformations I.2.3.2 Formal Definitions I.2.3.3 The Characteristic Equation I.2.3.4 Eigenvalues and Eigenvectors of a 2 x 2 Correlation Matrix I.2.3.5 Properties of Eigenvalues and Eigenvectors I.2.3.6 Using Excel to Find Eigenvalues and Eigenvectors I.2.3.7 Eigenvalue Test for Definiteness I.2.4 Applications to Linear Portfolios I.2.4.1 Covariance and Correlation Matrices I.2.4.2 Portfolio Risk and Return in Matrix Notation I.2.4.3 Positive Definiteness of Covariance and Correlation Matrices I.2.4.4 Eigenvalues and Eigenvectors of Covariance and Correlation Matrices I.2.5 Matrix Decomposition I.2.5.1 Spectral Decomposition of a Symmetric Matrix I.2.5.2 Similarity Transforms I.2.5.3 Cholesky Decomposition I.2.5.4 LU Decomposition I.2.6 Principal Component Analysis I.2.6.1 Definition of Principal Components I.2.6.2 Principal Component Representation I.2.6.3 Case Study: PCA of European Equity Indices I.2.7 Summary and Conclusions 37 37 38 38 39 40 41 43 44 45 46 48 48 50 51 52 52 53 54 55 55 56 58 59 61 61 62 62 63 64 65 66 67 70 1.3 Probability and Statistics I.3.1 Introduction I.3.2 Basic Concepts I.3.2.1 Classical versus Bayesian Approaches I.3.2.2 Laws of Probability I.3.2.3 Density and Distribution Functions I.3.2.4 Samples and Histograms I.3.2.5 Expected Value and Sample Mean I.3.2.6 Variance I.3.2.7 Skewness and Kurtosis I.3.2.8 Quantiles, Quartiles and Percentiles I.3.3 Univariate Distributions I.3.3.1 Binomial Distribution I.3.3.2 Poisson and Exponential Distributions I.3.3.3 Uniform Distribution I.3.3.4 Normal Distribution I.3.3.5 Lognormal Distribution I.3.3.6 Normal Mixture Distributions I.3.3.7 Student t Distributions I.3.3.8 Sampling Distributions I.3.3.9 Generalized Extreme Value Distributions I.3.3.10 Generalized Pareto Distribution I.3.3.11 Stable Distributions I.3.3.12 Kernels I.3.4 Multivariate Distributions I.3.4.1 Bivariate Distributions I.3.4.2 Independent Random Variables I.3.4.3 Covariance I.3.4.4 Correlation I.3.4.5 Multivariate Continuous Distributions I.3.4.6 Multivariate Normal Distributions I.3.4.7 Bivariate Normal Mixture Distributions I.3.4.8 Multivariate Student t Distributions I.3.5 Introduction to Statistical Inference I.3.5.1 Quantiles, Critical Values and Confidence Intervals I.3.5.2 Central Limit Theorem I.3.5.3 Confidence Intervals Based on Student t Distribution I.3.5.4 Confidence Intervals for Variance I.3.5.5 Hypothesis Tests I.3.5.6 Tests on Means I.3.5.7 Tests on Variances I.3.5.8 Non-Parametric Tests on Distributions I.3.6 Maximum Likelihood Estimation I.3.6.1 The Likelihood Function I.3.6.2 Finding the Maximum Likelihood Estimates I.3.6.3 Standard Errors on Mean and Variance Estimates 71 71 72 72 73 75 76 78 79 81 83 85 85 87 89 90 93 94 97 100 101 103 105 106 107 108 109 110 111 114 115 116 117 118 118 120 122 123 124 125 126 127 130 130 131 133 I.3.7 Stochastic Processes in Discrete and Continuous Time I.3.7.1 Stationary and Integrated Processes in Discrete Time I.3.7.2 Mean Reverting Processes and Random Walks in Continuous Time I.3.7.3 Stochastic Models for Asset Prices and Returns I.3.7.4 Jumps and the Poisson Process I.3.8 Summary and Conclusions 134 134 136 137 139 140 1.4 Introduction to Linear Regression I.4.1 Introduction I.4.2 Simple Linear Regression I.4.2.1 Simple Linear Model I.4.2.2 Ordinary Least Squares I.4.2.3 Properties of the Error Process I.4.2.4 ANOVA and Goodness of Fit I.4.2.5 Hypothesis Tests on Coefficients I.4.2.6 Reporting the Estimated Regression Model I.4.2.7 Excel Estimation of the Simple Linear Model I.4.3 Properties of OLS Estimators I.4.3.1 Estimates and Estimators I.4.3.2 Unbiasedness and Efficiency I.4.3.3 Gauss--Markov Theorem I.4.3.4 Consistency and Normality of OLS Estimators I.4.3.5 Testing for Normality I.4.4 Multivariate Linear Regression I.4.4.1 Simple Linear Model and OLS in Matrix Notation I.4.4.2 General Linear Model I.4.4.3 Case Study: A Multiple Regression I.4.4.4 Multiple Regression in Excel I.4.4.5 Hypothesis Testing in Multiple Regression I.4.4.6 Testing Multiple Restrictions I.4.4.7 Confidence Intervals I.4.4.8 Multicollinearity I.4.4.9 Case Study: Determinants of Credit Spreads I.4.4.10 Orthogonal Regression I.4.5 Autocorrelation and Heteroscedasticity I.4.5.1 Causes of Autocorrelation and Heteroscedasticity I.4.5.2 Consequences of Autocorrelation and Heteroscedasticity I.4.5.3 Testing for Autocorrelation I.4.5.4 Testing for Heteroscedasticity I.4.5.5 Generalized Least Squares I.4.6 Applications of Linear Regression in Finance I.4.6.1 Testing a Theory I.4.6.2 Analysing Empirical Market Behaviour I.4.6.3 Optimal Portfolio Allocation 143 143 144 144 146 148 149 151 152 153 155 155 156 157 157 158 158 159 161 162 163 163 166 167 170 171 173 175 175 176 176 177 178 179 179 180 181 I.4.6.4 Regression-Based Hedge Ratios I.4.6.5 Trading on Regression Models I.4.7 Summary and Conclusions I.5 Numerical Methods in Finance I.5.1 Introduction I.5.2 Iteration I.5.2.1 Method of Bisection I.5.2.2 Newton­Raphson Iteration I.5.2.3 Gradient Methods I.5.3 Interpolation and Extrapolation I.5.3.1 Linear and Bilinear Interpolation I.5.3.2 Polynomial Interpolation: Application to Currency Options I.5.3.3 Cubic Splines: Application to Yield Curves I.5.4 Optimization I.5.4.1 Least Squares Problems I.5.4.2 Likelihood Methods I.5.4.3 The EM Algorithm I.5.4.4 Case Study: Applying the EM Algorithm to Normal Mixture Densities I.5.5 Finite Difference Approximations I.5.5.1 First and Second Order Finite Differences I.5.5.2 Finite Difference Approximations for the Greeks I.5.5.3 Finite Difference Solutions to Partial Differential Equations I.5.6 Binomial Lattices I.5.6.1 Constructing the Lattice I.5.6.2 Arbitrage Free Pricing and Risk Neutral Valuation I.5.6.3 Pricing European Options I.5.6.4 Lognormal Asset Price Distributions I.5.6.5 Pricing American Options I.5.7 Monte Carlo Simulation I.5.7.1 Random Numbers I.5.7.2 Simulations from an Empirical or a Given Distribution I.5.7.3 Case Study: Generating Time Series of Lognormal Asset Prices I.5.7.4 Simulations on a System of Two Correlated Normal Returns I.5.7.5 Multivariate Normal and Student t Distributed Simulations I.5.8 Summary and Conclusions I.6 Introduction to Portfolio Theory I.6.1 Introduction I.6.2 Utility Theory I.6.2.1 Properties of Utility Functions I.6.2.2 Risk Preference I.6.2.3 How to Determine the Risk Tolerance of an Investor I.6.2.4 Coefficients of Risk Aversion 181 182 184 185 185 187 187 188 191 193 193 195 197 200 201 202 203 203 206 206 207 208 210 211 211 212 213 215 217 217 217 218 220 220 223 225 225 226 226 229 230 231 Some Standard Utility Functions Mean--Variance Criterion Extension of the Mean--Variance Criterion to Higher Moments I.6.3 Portfolio Allocation I.6.3.1 Portfolio Diversification I.6.3.2 Minimum Variance Portfolios I.6.3.3 The Markowitz Problem I.6.3.4 Minimum Variance Portfolios with Many Constraints I.6.3.5 Efficient Frontier I.6.3.6 Optimal Allocations I.6.4 Theory of Asset Pricing I.6.4.1 Capital Market Line I.6.4.2 Capital Asset Pricing Model I.6.4.3 Security Market Line I.6.4.4 Testing the CAPM I.6.4.5 Extensions to CAPM I.6.5 Risk Adjusted Performance Measures I.6.5.1 CAPM RAPMs I.6.5.2 Making Decisions Using the Sharpe Ratio I.6.5.3 Adjusting the Sharpe Ratio for Autocorrelation I.6.5.4 Adjusting the Sharpe Ratio for Higher Moments I.6.5.5 Generalized Sharpe Ratio I.6.5.6 Kappa Indices, Omega and Sortino Ratio I.6.6 Summary and Conclusions References Statistical Tables Index I.6.2.5 I.6.2.6 I.6.2.7 232 234 235 237 238 240 244 245 246 247 250 250 252 253 254 255 256 257 258 259 260 262 263 266 269 273 279 Market Risk Analysis Volume II Practical Financial Econometrics Contents List of Figures List of Tables List of Examples Foreword Preface to Volume II II.1 Factor Models II.1.1 Introduction II.1.2 Single Factor Models II.1.2.1 Single Index Model II.1.2.2 Estimating Portfolio Characteristics using OLS II.1.2.3 Estimating Portfolio Risk using EWMA II.1.2.4 Relationship between Beta, Correlation and Relative Volatility II.1.2.5 Risk Decomposition in a Single Factor Model II.1.3 Multi-Factor Models II.1.3.1 Multi-factor Models of Asset or Portfolio Returns II.1.3.2 Style Attribution Analysis II.1.3.3 General Formulation of Multi-factor Model II.1.3.4 Multi-factor Models of International Portfolios II.1.4 Case Study: Estimation of Fundamental Factor Models II.1.4.1 Estimating Systematic Risk for a Portfolio of US Stocks II.1.4.2 Multicollinearity: A Problem with Fundamental Factor Models II.1.4.3 Estimating Fundamental Factor Models by Orthogonal Regression II.1.5 Analysis of Barra Model II.1.5.1 Risk Indices, Descriptors and Fundamental Betas II.1.5.2 Model Specification and Risk Decomposition II.1.6 Tracking Error and Active Risk II.1.6.1 Ex Post versus Ex Ante Measurement of Risk and Return II.1.6.2 Definition of Active Returns II.1.6.3 Definition of Active Weights II.1.6.4 Ex Post Tracking Error xiii xvii xx xxii xxvi 1 1 2 2 4 6 8 10 11 11 13 16 17 21 22 23 25 27 28 30 31 32 32 33 33 II.1.6.5 Ex Post Mean-Adjusted Tracking Error II.1.6.6 Ex Ante Tracking Error II.1.6.7 Ex Ante Mean-Adjusted Tracking Error II.1.6.8 Clarification of the Definition of Active Risk II.1.7 Summary and Conclusions II.2 Principal Component Analysis II.2.1 Introduction II.2.2 Review of Principal Component Analysis II.2.2.1 Definition of Principal Components II.2.2.2 Principal Component Representation II.2.2.3 Frequently Asked Questions II.2.3 Case Study: PCA of UK Government Yield Curves II.2.3.1 Properties of UK Interest Rates II.2.3.2 Volatility and Correlation of UK Spot Rates II.2.3.3 PCA on UK Spot Rates Correlation Matrix II.2.3.4 Principal Component Representation II.2.3.5 PCA on UK Short Spot Rates Covariance Matrix II.2.4 Term Structure Factor Models II.2.4.1 Interest Rate Sensitive Portfolios II.2.4.2 Factor Models for Currency Forward Positions II.2.4.3 Factor Models for Commodity Futures Portfolios II.2.4.4 Application to Portfolio Immunization II.2.4.5 Application to Asset­Liability Management II.2.4.6 Application to Portfolio Risk Measurement II.2.4.7 Multiple Curve Factor Models II.2.5 Equity PCA Factor Models II.2.5.1 Model Structure II.2.5.2 Specific Risks and Dimension Reduction II.2.5.3 Case Study: PCA Factor Model for DJIA Portfolios II.2.6 Summary and Conclusions II.3 Classical Models of Volatility and Correlation II.3.1 Introduction II.3.2 Variance and Volatility II.3.2.1 Volatility and the Square-Root-of-Time Rule II.3.2.2 Constant Volatility Assumption II.3.2.3 Volatility when Returns are Autocorrelated II.3.2.4 Remarks about Volatility II.3.3 Covariance and Correlation II.3.3.1 Definition of Covariance and Correlation II.3.3.2 Correlation Pitfalls II.3.3.3 Covariance Matrices II.3.3.4 Scaling Covariance Matrices II.3.4 Equally Weighted Averages II.3.4.1 Unconditional Variance and Volatility II.3.4.2 Unconditional Covariance and Correlation II.3.4.3 Forecasting with Equally Weighted Averages 36 39 40 42 44 47 47 48 49 49 50 53 53 55 56 58 60 61 62 66 70 71 72 73 76 80 80 81 82 86 89 89 90 90 92 92 93 94 94 95 96 97 98 99 102 103 II.3.5 Precision of Equally Weighted Estimates II.3.5.1 Confidence Intervals for Variance and Volatility II.3.5.2 Standard Error of Variance Estimator II.3.5.3 Standard Error of Volatility Estimator II.3.5.4 Standard Error of Correlation Estimator II.3.6 Case Study: Volatility and Correlation of US Treasuries II.3.6.1 Choosing the Data II.3.6.2 Our Data II.3.6.3 Effect of Sample Period II.3.6.4 How to Calculate Changes in Interest Rates II.3.7 Equally Weighted Moving Averages II.3.7.1 Effect of Volatility Clusters II.3.7.2 Pitfalls of the Equally Weighted Moving Average Method II.3.7.3 Three Ways to Forecast Long Term Volatility II.3.8 Exponentially Weighted Moving Averages II.3.8.1 Statistical Methodology II.3.8.2 Interpretation of Lambda II.3.8.3 Properties of EWMA Estimators II.3.8.4 Forecasting with EWMA II.3.8.5 Standard Errors for EWMA Forecasts II.3.8.6 RiskMetricsTM Methodology II.3.8.7 Orthogonal EWMA versus RiskMetrics EWMA II.3.9 Summary and Conclusions II.4 Introduction to GARCH Models II.4.1 Introduction II.4.2 The Symmetric Normal GARCH Model II.4.2.1 Model Specification II.4.2.2 Parameter Estimation II.4.2.3 Volatility Estimates II.4.2.4 GARCH Volatility Forecasts II.4.2.5 Imposing Long Term Volatility II.4.2.6 Comparison of GARCH and EWMA Volatility Models II.4.3 Asymmetric GARCH Models II.4.3.1 A-GARCH II.4.3.2 GJR-GARCH II.4.3.3 Exponential GARCH II.4.3.4 Analytic E-GARCH Volatility Term Structure Forecasts II.4.3.5 Volatility Feedback II.4.4 Non-Normal GARCH Models II.4.4.1 Student t GARCH Models II.4.4.2 Case Study: Comparison of GARCH Models for the FTSE 100 II.4.4.3 Normal Mixture GARCH Models II.4.4.4 Markov Switching GARCH II.4.5 GARCH Covariance Matrices II.4.5.1 Estimation of Multivariate GARCH Models II.4.5.2 Constant and Dynamic Conditional Correlation GARCH II.4.5.3 Factor GARCH 104 104 106 107 109 109 110 111 112 113 115 115 117 118 120 120 121 122 123 124 126 128 129 131 131 135 135 137 141 142 144 147 147 148 150 151 154 156 157 157 159 161 163 164 165 166 169 II.4.6 Orthogonal GARCH II.4.6.1 Model Specification II.4.6.2 Case Study: A Comparison of RiskMetrics and O-GARCH II.4.6.3 Splicing Methods for Constructing Large Covariance Matrices II.4.7 Monte Carlo Simulation with GARCH Models II.4.7.1 Simulation with Volatility Clustering II.4.7.2 Simulation with Volatility Clustering Regimes 11.4.7.3 Simulation with Correlation Clustering II.4.8 Applications of GARCH Models II.4.8.1 Option Pricing with GARCH Diffusions II.4.8.2 Pricing Path-Dependent European Options II.4.8.3 Value-at-Risk Measurement II.4.8.4 Estimation of Time Varying Sensitivities II.4.8.5 Portfolio Optimization II.4.9 Summary and Conclusions II.5 Time Series Models and Cointegration II.5.1 Introduction II.5.2 Stationary Processes II.5.2.1 Time Series Models II.5.2.2 Inversion and the Lag Operator II.5.2.3 Response to Shocks II.5.2.4 Estimation II.5.2.5 Prediction II.5.2.6 Multivariate Models for Stationary Processes II.5.3 Stochastic Trends II.5.3.1 Random Walks and Efficient Markets II.5.3.2 Integrated Processes and Stochastic Trends II.5.3.3 Deterministic Trends II.5.3.4 Unit Root Tests II.5.3.5 Unit Roots in Asset Prices II.5.3.6 Unit Roots in Interest Rates, Credit Spreads and Implied Volatility II.5.3.7 Reconciliation of Time Series and Continuous Time Models II.5.3.8 Unit Roots in Commodity Prices II.5.4 Long Term Equilibrium II.5.4.1 Cointegration and Correlation Compared II.5.4.2 Common Stochastic Trends II.5.4.3 Formal Definition of Cointegration II.5.4.4 Evidence of Cointegration in Financial Markets II.5.4.5 Estimation and Testing in Cointegrated Systems II.5.4.6 Application to Benchmark Tracking II.5.4.7 Case Study: Cointegration Index Tracking in the Dow Jones Index II.5.5 Modelling Short Term Dynamics II.5.5.1 Error Correction Models 171 171 173 179 180 180 183 185 188 188 189 192 193 195 197 201 201 202 203 206 206 208 210 211 212 212 213 214 215 218 220 223 224 225 225 227 228 229 231 239 240 243 243 II.5.5.2 Granger Causality II.5.5.3 Case Study: Pairs Trading Volatility Index Futures II.5.6 Summary and Conclusions II.6 Introduction to Copulas II.6.1 Introduction II.6.2 Concordance Metrics II.6.2.1 Concordance II.6.2.2 Rank Correlations II.6.3 Copulas and Associated Theoretical Concepts II.6.3.1 Simulation of a Single Random Variable II.6.3.2 Definition of a Copula II.6.3.3 Conditional Copula Distributions and their Quantile Curves II.6.3.4 Tail Dependence II.6.3.5 Bounds for Dependence II.6.4 Examples of Copulas II.6.4.1 Normal or Gaussian Copulas II.6.4.2 Student t Copulas II.6.4.3 Normal Mixture Copulas II.6.4.4 Archimedean Copulas II.6.5 Conditional Copula Distributions and Quantile Curves II.6.5.1 Normal or Gaussian Copulas II.6.5.2 Student t Copulas II.6.5.3 Normal Mixture Copulas II.6.5.4 Archimedean Copulas II.6.5.5 Examples II.6.6 Calibrating Copulas II.6.6.1 Correspondence between Copulas and Rank Correlations II.6.6.2 Maximum Likelihood Estimation II.6.6.3 How to Choose the Best Copula II.6.7 Simulation with Copulas II.6.7.1 Using Conditional Copulas for Simulation II.6.7.2 Simulation from Elliptical Copulas II.6.7.3 Simulation with Normal and Student t Copulas II.6.7.4 Simulation from Archimedean Copulas II.6.8 Market Risk Applications II.6.8.1 Value-at-Risk Estimation II.6.8.2 Aggregation and Portfolio Diversification II.6.8.3 Using Copulas for Portfolio Optimization II.6.9 Summary and Conclusions II.7 Advanced Econometric Models II.7.1 Introduction II.7.2 Quantile Regression II.7.2.1 Review of Standard Regression II.7.2.2 What is Quantile Regression? II.7.2.3 Parameter Estimation in Quantile Regression 246 247 250 253 253 255 255 256 258 258 259 263 264 265 266 266 268 269 271 273 273 274 275 275 276 279 280 281 283 285 285 286 287 290 290 291 292 295 298 301 301 303 304 305 305 II.7.2.4 Inference on Linear Quantile Regressions II.7.2.5 Using Copulas for Non-linear Quantile Regression II.7.3 Case Studies on Quantile Regression II.7.3.1 Case Study 1: Quantile Regression of Vftse on FTSE 100 Index II.7.3.2 Case Study 2: Hedging with Copula Quantile Regression II.7.4 Other Non-Linear Regression Models II.7.4.1 Non-linear Least Squares II.7.4.2 Discrete Choice Models II.7.5 Markov Switching Models II.7.5.1 Testing for Structural Breaks II.7.5.2 Model Specification II.7.5.3 Financial Applications and Software II.7.6 Modelling Ultra High Frequency Data II.7.6.1 Data Sources and Filtering II.7.6.2 Modelling the Time between Trades II.7.6.3 Forecasting Volatility II.7.7 Summary and Conclusions II.8 Forecasting and Model Evaluation II.8.1 Introduction II.8.2 Returns Models II.8.2.1 Goodness of Fit II.8.2.2 Forecasting II.8.2.3 Simulating Critical Values for Test Statistics II.8.2.4 Specification Tests for Regime Switching Models II.8.3 Volatility Models II.8.3.1 Goodness of Fit of GARCH Models II.8.3.2 Forecasting with GARCH Volatility Models II.8.3.3 Moving Average Models II.8.4 Forecasting the Tails of a Distribution II.8.4.1 Confidence Intervals for Quantiles II.8.4.2 Coverage Tests II.8.4.3 Application of Coverage Tests to GARCH Models II.8.4.4 Forecasting Conditional Correlations II.8.5 Operational Evaluation II.8.5.1 General Backtesting Algorithm II.8.5.2 Alpha Models II.8.5.3 Portfolio Optimization II.8.5.4 Hedging with Futures II.8.5.5 Value-at-Risk Measurement II.8.5.6 Trading Implied Volatility II.8.5.7 Trading Realized Volatility II.8.5.8 Pricing and Hedging Options II.8.6 Summary and Conclusions References Index 307 307 309 309 314 319 319 321 325 325 327 329 330 330 332 334 337 341 341 342 343 347 348 350 350 351 352 354 356 356 357 360 361 363 363 365 366 366 367 370 372 373 375 377 387 Market Risk Analysis Volume III Pricing, Hedging and Trading Financial Instruments Contents List of Figures List of Tables List of Examples Foreword Preface to Volume III III.1 Bonds and Swaps III.1.1 Introduction III.1.2 Interest Rates III.1.2.1 Continuously Compounded Spot and Forward Rates III.1.2.2 Discretely Compounded Spot Rates III.1.2.3 Translation between Discrete Rates and Continuous Rates III.1.2.4 Spot and Forward Rates with Discrete Compounding III.1.2.5 LIBOR III.1.3 Categorization of Bonds III.1.3.1 Categorization by Issuer III.1.3.2 Categorization by Coupon and Maturity III.1.4 Characteristics of Bonds and Interest Rates III.1.4.1 Present Value, Price and Yield III.1.4.2 Relationship between Price and Yield III.1.4.3 Yield Curves III.1.4.4 Behaviour of Market Interest Rates III.1.4.5 Characteristics of Spot and Forward Term Structures III.1.5 Duration and Convexity III.1.5.1 Macaulay Duration III.1.5.2 Modified Duration III.1.5.3 Convexity III.1.5.4 Duration and Convexity of a Bond Portfolio 24 III.1.5.5 Duration--Convexity Approximations to Bond Price Change III.1.5.6 Immunizing Bond Portfolios xiii xvii xix xxi xxv 1 1 2 3 4 6 6 8 8 9 10 10 11 13 14 17 19 20 21 23 24 25 27 III.I.6 Bonds with Semi-Annual and Floating Coupons III.I.6.1 Semi-Annual and Quarterly Coupons III.I.6.2 Floating Rate Notes III.I.6.3 Other Floaters III.I.7 Forward Rate Agreements and Interest Rate Swaps III.I.7.1 Forward Rate Agreements III.I.7.2 Interest Rate Swaps III.I.7.3 Cash Flows on Vanilla Swaps III.I.7.4 Cross-Currency Swaps III.I.7.5 Other Swaps III.I.8 Present Value of Basis Point III.I.8.1 PV01 and Value Duration III.I.8.2 Approximations to PV01 III.I.8.3 Understanding Interest Rate Risk III.I.9 Yield Curve Fitting III.I.9.1 Calibration Instruments III.I.9.2 Bootstrapping III.I.9.3 Splines III.I.9.4 Parametric Models III.I.9.5 Case Study: Statistical Properties of Forward LIBOR Rates III.I.10 Convertible Bonds 111.1.10.1 Characteristics of Convertible Bonds 111.1.10.2 Survey of Pricing Models for Convertible Bonds III.I.1 1 Summary and Conclusions 111.2 Futures and Forwards III.2.1 Introduction III.2.2 Characteristics of Futures and Forwards III.2.2.1 Interest Rate and Swap Futures III.2.2.2 Bond Futures III.2.2.3 Currency Futures and Forwards III.2.2.4 Energy and Commodity Futures III.2.2.5 Stock Futures and Index Futures III.2.2.6 Exchange Traded Funds and ETF Futures III.2.2.7 New Futures Markets III.2.3 Theoretical Relationships between Spot, Forward and Futures III.2.3.1 No Arbitrage Pricing III.2.3.2 Accounting for Dividends III.2.3.3 Dividend Risk and Interest Rate Risk III.2.3.4 Currency Forwards and the Interest Rate Differential III.2.3.5 No Arbitrage Prices for Forwards on Bonds III.2.3.6 Commodity Forwards, Carry Costs and Convenience Yields III.2.3.7 Fair Values of Futures and Spot III.2.4 The Basis III.2.4.1 No Arbitrage Range 28 29 31 33 33 34 35 36 38 40 41 41 44 45 48 48 49 51 52 53 59 60 61 62 65 65 68 68 70 73 74 79 80 82 87 87 88 90 91 92 93 94 95 95 III.2.4.2 Correlation between Spot and Futures Returns III.2.4.3 Introducing Basis Risk III.2.4.4 Basis Risk in Commodity Markets III.2.5 Hedging with Forwards and Futures III.2.5.1 Traditional 'Insurance' Approach III.2.5.2 Mean--Variance Approach III.2.5.3 Understanding the Minimum Variance Hedge Ratio III.2.5.4 Position Risk III.2.5.5 Proxy Hedging III.2.5.6 Basket Hedging III.2.5.7 Performance Measures for Hedged Portfolios III.2.6 Hedging in Practice III.2.6.1 Hedging Forex Risk III.2.6.2 Hedging International Stock Portfolios III.2.6.3 Case Study: Hedging an Energy Futures Portfolio III.2.6.4 Hedging Bond Portfolios III.2.7 Using Futures for Short Term Hedging III.2.7.1 Regression Based Minimum Variance Hedge Ratios III.2.7.2 Academic Literature on Minimum Variance Hedging III.2.7.3 Short Term Hedging in Liquid Markets III.2.8 Summary and Conclusions III.3 Options III.3.1 Introduction III.3.2 Foundations III.3.2.1 Arithmetic and Geometric Brownian Motion III.3.2.2 Risk Neutral Valuation III.3.2.3 Numeraire and Measure III.3.2.4 Market Prices and Model Prices III.3.2.5 Parameters and Calibration III.3.2.6 Option Pricing: Review of the Binomial Model III.3.3 Characteristics of Vanilla Options III.3.3.1 Elementary Options III.3.3.2 Put--Call Parity III.3.3.3 Moneyness III.3.3.4 American Options III.3.3.5 Early Exercise Boundary III.3.3.6 Pricing American Options III.3.4 Hedging Options III.3.4.1 Delta III.3.4.2 Delta Hedging III.3.4.3 Other Greeks III.3.4.4 Position Greeks III.3.4.5 Delta--Gamma Hedging III.3.4.6 Delta--Gamma--Vega Hedging III.3.5 Trading Options III.3.5.1 Bull Strategies 97 98 100 101 102 104 106 108 110 111 112 113 113 114 118 124 126 127 129 131 133 137 137 139 140 142 144 146 147 148 151 152 153 154 155 156 158 159 159 161 161 163 164 165 167 167 III.3.5.2 Bear Strategies III.3.5.3 Other Spread Strategies III.3.5.4 Volatility Strategies III.3.5.5 Replication of PandL Profiles III.3.6 The Black­Scholes­Merton Model III.3.6.1 Assumptions III.3.6.2 Black­Scholes­Merton PDE III.3.6.3 Is the Underlying the Spot or the Futures Contract? III.3.6.4 Black­Scholes­Merton Pricing Formula III.3.6.5 Interpretation of the Black­Scholes­Merton Formula III.3.6.6 Implied Volatility III.3.6.7 Adjusting BSM Prices for Stochastic Volatility III.3.7 The Black­Scholes­Merton Greeks III.3.7.1 Delta III.3.7.2 Theta and Rho III.3.7.3 Gamma III.3.7.4 Vega, Vanna and Volga III.3.7.5 Static Hedges for Standard European Options III.3.8 Interest Rate Options III.3.8.1 Caplets and Floorlets III.3.8.2 Caps, Floors and their Implied Volatilities III.3.8.3 European Swaptions III.3.8.4 Short Rate Models III.3.8.5 LIBOR Model III.3.8.6 Case Study: Application of PCA to LIBOR Model Calibration III.3.9 Pricing Exotic Options III.3.9.1 Pay-offs to Exotic Options III.3.9.2 Exchange Options and Best/Worst of Two Asset Options III.3.9.3 Spread Options III.3.9.4 Currency Protected Options III.3.9.5 Power Options III.3.9.6 Chooser Options and Contingent Options III.3.9.7 Compound Options III.3.9.8 Capped Options and Ladder Options III.3.9.9 Look-Back and Look-Forward Options III.3 .9. 1 0 Barrier Options III.3.9.1 1 Asian Options III.3.10 Summary and Conclusions 168 169 170 172 173 174 175 176 178 180 183 183 186 187 188 189 190 193 194 195 196 198 199 201 203 207 208 209 211 213 214 214 216 216 218 219 221 224 111.4 Volatility III.4.1 Introduction III.4.2 Implied Volatility III.4.2.1 'Backing Out' Implied Volatility from a Market Price III.4.2.2 Equity Index Volatility Skew III.4.2.3 Smiles and Skews in Other Markets 227 227 231 231 233 236 III.4.2.4 Term Structures of Implied Volatilities III.4.2.5 Implied Volatility Surfaces III.4.2.6 Cap and Caplet Volatilities III.4.2.7 Swaption Volatilities III.4.3 Local Volatility III.4.3.1 Forward Volatility III.4.3.2 Dupire's Equation III.4.3.3 Parametric Models of Local Volatility III.4.3.4 Lognormal Mixture Diffusion III.4.4 Modelling the Dynamics of Implied Volatility III.4.4.1 Sticky Models III.4.4.2 Case Study I: Principal Component Analysis of Implied Volatilities III.4.4.3 Case Study II: Modelling the ATM Volatility--Index Relationship III.4.4.4 Case Study III: Modelling the Skew Sensitivities III.4.4.5 Applications of Implied Volatility Dynamics to Hedging Options III.4.5 Stochastic Volatility Models III.4.5.1 Stochastic Volatility PDE III.4.5.2 Properties of Stochastic Volatility III.4.5.3 Model Implied Volatility Surface III.4.5.4 Model Local Volatility Surface III.4.5.5 Heston Model III.4.5.6 GARCH Diffusions III.4.5.7 CEV and SABR Models III.4.5.8 Jumps in Prices and in Stochastic Volatility III.4.6 Scale Invariance and Hedging III.4.6.1 Scale Invariance and Change of Numeraire III.4.6.2 Definition of Scale Invariance III.4.6.3 Scale Invariance and Homogeneity III.4.6.4 Model Free Price Hedge Ratios III.4.6.5 Minimum Variance Hedging III.4.6.6 Minimum Variance Hedge Ratios in Specific Models III.4.6.7 Empirical Results III.4.7 Trading Volatility III.4.7.1 Variance Swaps and Volatility Swaps III.4.7.2 Trading Forward Volatility III.4.7.3 Variance Risk Premium III.4.7.4 Construction of a Volatility Index III.4.7.5 Effect of the Skew III.4.7.6 Term Structures of Volatility Indices III.4.7.7 Vix and Other Volatility Indices III.4.7.8 Volatility Index Futures III.4.7.9 Options on Volatility Indices III.4.7.10 Using Realized Volatility Forecasts to Trade Volatility III.4.8 Summary and Conclusion 238 239 240 242 243 244 245 248 249 255 255 257 261 264 265 268 269 271 275 277 278 280 285 287 289 291 291 292 294 297 299 300 303 304 306 307 308 309 309 311 312 314 315 316 III.5 Portfolio Mapping III.5.1 Introduction III.5.2 Risk Factors and Risk Factor Sensitivities III.5.2.1 Interest Rate Sensitive Portfolios III.5.2.2 Equity Portfolios III.5.2.3 International Exposures III.5.2.4 Commodity Portfolios III.5.2.5 Options Portfolios III.5.2.6 Orthogonalization of Risk Factors III.5.2.7 Nominal versus Percentage Risk Factors and Sensitivities III.5.3 Cash Flow Mapping III.5.3.1 Present Value Invariant and Duration Invariant Maps III.5.3.2 PV01 Invariant Cash Flow Maps III.5.3.3 Volatility Invariant Maps III.5.3.4 Complex Cash Flow Maps III.5.4 Applications of Cash Flow Mapping to Market Risk Management III.5.4.1 Risk Management of Interest Rate Sensitive Portfolios III.5.4.2 Mapping Portfolios of Commodity Futures III.5.5 Mapping an Options Portfolio to Price Risk Factors III.5.5.1 Taylor Expansions III.5.5.2 Value Delta and Value Gamma III.5.5.3 Delta--Gamma Approximation: Single Underlying III.5.5.4 Effect of Gamma on Portfolio Risk III.5.5.5 Price Beta Mapping III.5.5.6 Delta--Gamma Approximation: Several Underlyings III.5.5.7 Including Time and Interest Rates Sensitivities III.5.6 Mapping Implied Volatility III.5.6.1 Vega Risk in Options Portfolios III.5.6.2 Second Order Approximations: Vanna and Volga III.5.6.3 Vega Bucketing III.5.6.4 Volatility Beta Mapping III.5.7 Case Study: Volatility Risk in FTSE 100 Options III.5.7.1 Estimating the Volatility Betas III.5.7.2 Model Risk of Volatility Mapping III.5.7.3 Mapping to Term Structures of Volatility Indices III.5.7.4 Using PCA with Volatility Betas III.5.8 Summary and Conclusions References Index 321 321 323 323 324 327 328 328 330 330 332 332 333 334 336 337 337 338 340 341 342 344 346 347 349 351 353 353 354 355 356 357 357 360 361 361 364 367 377

There are no comments for this item.

Log in to your account to post a comment.
Koha 18.11 - INSEAD Catalogue
Home | Contact Us | What's Koha?