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Value-at-Risk
Theory and Practice
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Cover
Cover Page
Copyright
Contents
0 Preface
0.1 What We’re About
0.2 Contents Overview
0.3 Audience
0.4 How to Read the Book
0.5 Notation and Terminology
0.6 Acknowledgments
1 Value-at-Risk
1.1 History
1.2 Measures
1.3 Risk Measures
1.4 Market Risk
1.5 Value-at-Risk
1.6 Risk Limits
1.7 Examples
1.8 VaR Measures
1.9 Further Reading
2 Mathematical Preliminaries
2.1 Motivation
2.2 Notation and Terminology
2.3 Gradient and Gradient-Hessian Approximations
2.4 Ordinary Interpolation
2.5 Complex Numbers
2.6 Eigenvalues and Eigenvectors
2.7 Cholesky Factorization
2.8 Minimizing a Quadratic Polynomial
2.9 Ordinary Least Squares
2.10 Cubic Spline Interpolation
2.11 Finite Difference Approximations for Derivatives
2.12 Newton’s Method
2.13 Change of Variables Formula
2.14 Numerical Integration in One Dimension
2.15 Numerical Integration in Multiple Dimensions
2.16 Further Reading
3 Probability
3.1 Motivation
3.2 Prerequisites
3.3 Parameters
3.4 Parameters of Random Vectors
3.5 Linear Polynomials of Random Vectors
3.6 Properties of Random Vectors
3.7 Principal Component Analysis
3.8 Uniform and Related Distributions
3.9 Normal and Related Distributions
3.10 Mixtures of Distributions
3.11 Moment-Generating Distributions
3.12 Quadratic Polynomials of Joint-Normal Random Vectors
3.13 The Cornish-Fisher Expansion
3.14 Central Limit Theorem
3.15 The Inversion Theorem
3.16 Quantiles of Quadratic Polynomials of Joint-Normal Random Vectors
3.17 Further Reading
4 Statistics and Time Series Analysis
4.1 Motivation
4.2 From Probability to Statistics
4.3 Estimation
4.4 Maximum Likelihood Estimators
4.5 Stochastic Processes
4.6 White Noise, Autoregressive, and Moving-Average Processes
4.7 GARCH Processes
4.8 Regime-Switching Processes
4.9 Further Reading
5 Monte Carlo Method
5.1 Motivation
5.2 The Monte Carlo Method
5.3 Realizations of Samples
5.4 Pseudorandom Numbers
5.5 Testing Pseudorandom Number Generators
5.6 Implementing Pseudorandom Number Generators
5.7 Breaking the Curse of Dimensionality
5.8 Pseudorandom Variates
5.9 Variance Reduction
5.10 Further Reading
6 Market Data
6.1 Motivation
6.2 Forms of Data
6.3 Nonsynchronous Data
6.4 Data Errors
6.5 Data Bias
6.6 Futures
6.7 Implied Volatilities
6.8 Further Reading
7 Inference
7.1 Motivation
7.2 Selecting Key Factors
7.3 Current Practice
7.4 Unconditional Leptokurtosis and Conditional Heteroskedasticity
7.5 Historical Realizations
7.6 Further Reading
8 Primary Mappings
8.1 Motivation
8.2 Day Counts
8.3 Primary Mappings
8.4 Example: Equities
8.5 Example: Forwards
8.6 Example: Options
8.7 Example: Physical Commodities
8.8 Further Reading
9 Remappings
9.1 Motivation
9.2 Holdings Remappings
9.3 Global Remappings
9.4 Change-of-Variables Remappings
9.5 Principal-Component Remappings
9.6 Further Reading
10 Transformations
10.1 Motivation
10.2 Linear Transformation Procedures
10.3 Quadratic Transformation Procedures
10.4 Monte Carlo Transformation Procedures
10.5 Variance Reduction
10.6 Further Reading
Back Matter
Standard Normal Table
References
Index
Author:
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