, ®
@GARP
FRM I Financial Risk Manager
2024
®
EXAM PART II
Market Risk
Measurement
and Management
@Pearson
,Excerpts taken from:
Options, Futures, and Other Derivatives, Tenth Edition by John C. Hull
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"Estimating Market Risk Measures," "Non-Parametric Approaches," and "Parametric Approaches (Ill): Extreme
Value" by Kevin Dowd, reprinted from Measuring Market Risk, Second Edition (2005), by permission of John
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"Back Testing VaR" and "VaR Mapping," by Philippe Jorion, reprinted from Value at Risk: The New Benchmark
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"Messages from the Academic Literature on Risk Measurement for the Trading Book," Working Paper No. 19
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"Some Correlation Basics: Definitions, Applications, and Terminology," "Empirical Properties of Correlation:
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"Empirical Approaches to Risk Metrics and Hedges," "The Science of Term Structure Models," "The Evolution
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"Fundamental Review of the Trading Book," by John C. Hull, reprinted from Risk Management and Financial
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@Pearson ISBN 10: 0-13-829218-3
ISBN 13: 978-0-13-829218-8
, Contents
1.6 The Core Issues: An Overview 13
Chapter 1 Estimating Market
1. 7 Appendix 13
Risk Measures 1
Preliminary Data Analysis 13
Plotting the Data and Evaluating
Summary Statistics 14
1.1 Data 2
QQ Plots 14
Profit/Loss Data 2
Loss/Profit Data 2
Arithmetic Return Data 2 Chapter 2 Non-Parametric
Geometric Return Data 2 Approaches 17
1 .2 Estimating Historical
Simulation VaR 3
2.1 Compiling Historical
1 .3 Estimating Parametric VaR 4 Simulation Data 18
Estimating VaR with Normally Distributed
Profits/Losses 4 2.2 Estimation of Historical
Estimating VaR with Normally Distributed Simulation VaR and ES 19
Arithmetic Returns 5 Basic Historical Simulation 19
Estimating Lognormal VaR 6 Bootstrapped Historical Simulation 19
Historical Simulation Using
1.4 Estimating Coherent Risk Measures 7
Non-parametric Density Estimation 19
Estimating Expected Shortfall 7
Estimating Curves and Surfaces for
Estimating Coherent Risk Measures 8 VaR and ES 21
1 .5 Estimating the Standard Errors 2.3 Estimating Confidence Intervals
of Risk Measure Estimators 10 for Historical Simulation VaR and ES 21
Standard Errors of Quantile Estimators 10 An Order Statistics Approach to the
Standard Errors in Estimators of Estimation of Confidence Intervals for
Coherent Risk Measures 12 HS VaR and ES 22
iii
