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Value-at-Risk

Theory and Practice

  • 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

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Author: var

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