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Elsevier

Value at Risk

Theory and Practice

  • 1st Edition - February 26, 2003
  • Latest edition
  • Author: Glyn A. Holton
  • Language: English

Value at Risk is the first advanced book published on value-at-risk (VaR). It describes the ways to design, implement, and use scalable production VaR measures on actual trading f… Read more

Description

Value at Risk is the first advanced book published on value-at-risk (VaR). It describes the ways to design, implement, and use scalable production VaR measures on actual trading floors.

It takes readers from the basics of VaR to the most advanced techniques, many of which have never been published in book form. Practical, detailed examples are drawn from markets around the world, including: Euro deposits, Pacific Basin equities, physical coffees, and North American natural gas. Real-world challenges relating to market data, portfolio mappings, multicollinearity, and intra-horizon events are addressed in detail. Exercises reinforce concepts and walk readers step-by-step through computations. Sophisticated techniques are fully disclosed, including quadratic (delta-gamma) methods for nonlinear portfolios, variance reduction (control variates and stratified sampling) for Monte Carlo VaR measures, principal component remappings, techniques to fix estimated covariance matrices that are not positive-definite, the Cornish-Fisher expansion, and orthogonal GARCH.

This text is ideal for finance professionals around the world, finance professors, and students.

Key features

* First advanced text on Value-at-Risk * Practical, detailed examples drawn from markets around the world* Exercises reinforce concepts and walk readers step-by-step through computations

Readership

Finance professionals around the world; finance professors and students

Table of contents

PART ONE: OVERVIEW Preface: What We're About; Contents Overview; Audience; How to Read the Book; Notation and Terminology1. Value-at-Risk: History; Measures; Risk Measures; Market Risk; Value-at-Risk; Risk Limits; Examples; VaR Measures.PART TWO: ESSENTIAL MATHEMATICS2. Mathematical Preliminaries: Notation and Terminology; Gradient and Gradient-Hessian Approximations; Ordinary Interpolation; Complex Numbers; Eigenvalues and Eigenvectors; Cholesky Factorization; Minimizing a Quadratic Polynomial;Ordinary Least Squares; Cubic Spline Interpolation; Finite Difference Approximations of Derivatives; Newton's Method; Change of Variables Formula; Numerical Integration in One Dimension; Numerical Integration in Multiple Dimensions.3. Probability: Prerequisites; Parameters; Parameters of Random Vectors; Linear Polynomials of Random Vectors; Properties of Covariance Matrices; Principal Component Analysis; Uniform and Related Distributions; Normal and Related Distributions; Mixtures of Distributions; Moment-Generating Functions; Quadratic Polynomials of Joint-Normal Random Vectors; The Cornish-Fisher Expansion; Central Limit Theorem; The Inversion Theorem; Quantiles of Quadratic Polynomials of Joint-Normal Random Vectors.4. Statistics and Time Series Analysis: From Probability to Statistics; Estimation; Maximum Likelihood Estimators; Stochastic Processes; White Noise, Autoregressive and Moving Average Processes;GARCH Processes; Regime-Switching Processes.5. Monte Carlo Method: The Monte Carlo Method; Realizations of Samples; Pseudorandom Numbers; Testing Pseudorandom Number Generators; Implementing Pseudorandom Number Generators; Breaking the Curse of Dimensionality; Pseudorandom Variates; Variance Reduction.PART THREE: VALUE-AT-RISK6. Market Data: Forms of Data; Nonsynchronous Data; Data Errors; Data Biases; Futures; Implied Volatilities.7. Inference: Selecting Key Factors; Current Practice; Unconditional Leptokurtosis and Conditional Heteroskedasticity; Historical Realizations.8. Primary Mappings:Day Counts; Primary Mappings; Example: Equities; Example: Forwards; Example: Options; Example: Physical Commodities.9. Remappings: Holdings Remappings; Global Remappings; Change-of-Variables Remappings; Principal-Component Remappings.10. Transformations: Linear Transformation Procedures; Quadratic Transformation Procedures; Monte Carlo Transformation Procedures; Variance Reduction.

Product details

  • Edition: 1
  • Latest edition
  • Published: February 26, 2003
  • Language: English

About the author

GH

Glyn A. Holton

Glyn A. Holton is an independent consultant specializing in financial risk management. He formed his practice in 1995, and has since worked with hundreds of professionals in implementing value-at-risk and related solutions. Previously, he was a market risk manager for the Bank of Boston, a vice president for Fidelity Investments and an actuarial associate for Metropolitan Life. He holds a masters degree in mathematics from Temple University."
Affiliations and expertise
Contingency Analysis, Boston, Massachusetts, U.S.A.