Market risk analysis: 4 Value-at-risk models
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| Format: | Book |
| Language: | English |
| Published: |
Chichester [u.a.]
Wiley
2008
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| Online Access: | Inhaltsverzeichnis |
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| Physical Description: | XLII, 449 S. graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 9780470997888 |
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| 020 | |a 9780470997888 |9 978-0-470-99788-8 | ||
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| 100 | 1 | |a Alexander, Carol |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Market risk analysis |n 4 |p Value-at-risk models |c Carol Alexander |
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 2008 | |
| 300 | |a XLII, 449 S. |b graph. Darst. |e 1 CD-ROM (12 cm) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016480080 | ||
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| adam_text | Contents
List of
Figures
xiii
List of Tables
xvi
List of Examples
xxi
Foreword
xxv
Preface to Volume IV
xxix
IV.l Value at Risk and Other Risk Metrics
1
IV.
1.1
Introduction
1
IV.
1.2
An Overview of Market Risk Assessment
4
IV.
1.2.1
Risk Measurement in Banks
4
IV.
1.2.2
Risk Measurement in Portfolio Management
6
IV.
1.2.3
Risk Measurement in Large Corporations
7
IV.
1.3
Downside and Quantile Risk Metrics
9
IV.
1.3.1
Semi-Standard Deviation and Second Order Lower
Partial Moment
9
TVÄ.
3.2
Other Lower Partial Moments
10
IV.
1.3.3
Quantile Risk Metrics
П
IV.
1.4
Defining Value at Risk
1
3
IV.
1.4.1
Confidence Level and Risk Horizon
13
IV.l.
4.2
Discounted P&L 15
IV.
1.4.3
Mathematical Definition of VaR
15
IV.
1.5
Foundations of Value-at-Risk Measurement
17
IV.l.
5.1
Normal Linear VaR Formula: Portfolio Level
18
IV.
1.5.2
Static Portfolios 20
IV.1.5.3
Scaling VaR 21
IV.
1.5.4
Discounting and the Expected Return
23
IV.
1.6
Risk Factor Value at Risk 25
IV.
1.6.1
Motivation 26
IV.
1.6.2
Normal Linear Equity VaR 27
IV.
1.6.3
Normal Linear Interest Rate VaR 29
Vlil
Contents
IV.
1.7
Decomposition of Value at Risk
30
IV.
1.7.1
Systematic and Specific VaR
31
IV.
1.7.2
Stand-alone VaR
31
IV.
1.7.3
Marginal and Incremental VaR
32
IV.
1.8
Risk Metrics Associated with Value at Risk
33
IV.
1.8.1
Benchmark VaR
34
IV.
1.8.2
Conditional VaR: Expected Tail Loss and Expected
Shortfall
35
IV.
1.8.3
Coherent Risk Metrics
38
IV.
1.9
Introduction to Value-at-Risk Models
41
IV.1.9.1 Normal Linear VaR
41
IV.
1.9.2
Historical Simulation
42
IV.
1.9.3
Monte Carlo Simulation
44
IV.
1.9.4
Case Study: VaR of the S&P
500
Index
45
I V.I
.10
Summary and Conclusions
47
IV.2 Parametric Linear VaR Models
53
IV.2.1 Introduction
53
IV.2.2 Foundations of Normal Linear Value at Risk
56
IV.2.2.
1
Understanding the Normal Linear VaR Formula
56
IV.2.2.2 Analytic Formula for Normal VaR when Returns are
Autocorrelated
60
IV.2.2.3 Systematic Normal Linear VaR
63
IV.2.2.4 Stand-Alone Normal Linear VaR
64
IV.2.2.5 Marginal and Incremental Normal Linear VaR
66
IV.2.3 Normal Linear Value at Risk for Cash-Flow Maps
67
IV.2.3.
1
Normal Linear Interest Rate VaR
67
IV.2.3.2 Calculating PV01
68
IV.2.3.3 Approximating Marginal and Incremental VaR
70
IV.2.3.4 Disaggregating Normal Linear Interest Rate VaR
72
IV.2.3.5 Normal Linear Credit Spread VaR
75
IV.2.4 Case Study: PC Value at Risk of a UK Fixed Income Portfolio
79
IV.2.4.
1
Calculating the Volatility and VaR of the Portfolio
80
IV.2.4.2 Combining Cash-Flow Mapping with PC A
81
IV.2.4.3 Advantages of Using PC Factors for Interest Rate VaR
85
IV.2.5 Normal Linear Value at Risk for Stock Portfolios
85
IV.2.5.
1
Cash Positions on a Few Stocks
86
IV.2.5.2 Systematic and Specific VaR for Domestic Stock
Portfolios
87
IV.2.5.3 Empirical Estimation of Specific VaR
90
IV.2.5.4 EWMA Estimates of Specific VaR
91
IV.2.6 Systematic Value-at-Risk Decomposition for Stock Portfolios
93
IV.2.6.
1
Portfolios Exposed to One Foreign Currency
93
IV.2.6.2 Portfolios Exposed to Several Foreign Currencies
97
I V.2.6.3 Interest Rate VaR of Equity Portfolios
100
IV.2.6.4 Hedging the Risks of International Equity Portfolios
101
IV.2.7 Case Study: Normal Linear Value at Risk for Commodity Futures
103
Contents
IV.2.8 Student
t
Distributed
Linear
Value at Risk
106
IV.2.8.1 Effect ofLeptokurtosis and Skewness on VaR
106
IV.2.8.2 Student
t
Linear VaR Formula
107
IV.2.8.3 Empirical Examples of Student
t
Linear VaR
109
IV.2.9 Linear Value at Risk with Mixture Distributions 111
IV.2.9.
1
Mixture Distributions
111
IV.2.9.2 Mixture Linear VaR Formula
113
IV.2.9.3 Mixture Parameter Estimation
114
IV.2.9.4 Examples of Mixture Linear VaR
115
IV.2.9.5 Normal Mixture Risk Factor VaR
119
IV.2.
10
Exponential Weighting with Parametric Linear Value at Risk
121
IV.2.10.1 Exponentially Weighted Moving Averages
121
IV.2.10.2 EWMA VaR at the Portfolio Level
124
IV.2.
10.3
RiskMetrics™ VaR Methodology
126
IV.2.
11
Expected Tail Loss (Conditional VaR)
128
IV.2.
11.1
ETL in the Normal Linear VaR Model
129
IV.2.11.2 ETL in the Student
t
Linear VaR Model
130
IV.2.
11.3
ETL in the Normal Mixture Linear VaR Model
132
IV.2.
11.4
ETL under a Mixture of Student
t
Distributions
133
IV.2.
12
Case Study: Credit Spread Parametric Linear Value at Risk and ETL
135
IV.2.12.1 The iTraxx Europe Index
135
IV.2.
12.2
VaR Estimates
137
IV.2.13 Summary and Conclusions
138
IV.3 ffistorical Simulation
141
IV.3.1 Introduction
141
IV.3.2 Properties of Historical Value at Risk
144
IV.3.2.1 Definition of Historical VaR
144
IV.3.2.2 Sample Size and Data Frequency
145
IV.3.2.3 Power Law Scale Exponents
146
IV.3.2.4 Case Study: Scale Exponents for Major Risk Factors
147
IV.3.2.5 Scaling Historical VaR for Linear Portfolios
150
IV.3.2.6 Errors from Square-Root Scaling of Historical VaR
151
IV.3.2.7 Overlapping Data and Multi-Step Historical Simulation
151
IV.3.3 Improving the Accuracy of Historical Value at Risk
152
IV.3.3.1 Case Study: Equally Weighted Historical and Linear VaR
153
IV.3.3.2 Exponential Weighting of Return Distributions
156
IV.3.3.3 Volatility Adjustment
158
IV.3.3.4 Filtered Historical Simulation
163
IV.3.4 Precision of Historical Value at Risk at Extreme Quantiles
165
IV.3.4.1 Kernel Fitting
165
IV.3.
4.2
Extreme Value Distributions
167
IV.3.4.3 Cornish-Fisher Approximation
170
IV.3.4.4 Johnson Distributions
172
IV.3
.5
Historical Value at Risk for Linear Portfolios
175
rv.3.5.1 Historical VaR for Cash Flows
176
rv.3.5.2 Total, Systematic and Specific VaR of a Stock Portfolio
179
Contents
IV.3.5.3
Equity and Forex VaR of an International Stock Portfolio
185
IV.3.5.4 Interest Rate and Forex VaR of an International Bond
Position
190
IV.3.5.5 Case Study: Historical VaR for a Crack Spread Trader
192
IV.3.6 Estimating Expected Tail Loss in the Historical Value-at-Risk Model
195
IV.3.6.1 Parametric Historical ETL
195
IV.3.6.2 Empirical Results on Historical ETL
195
IV.3.6.3 Disaggregation of Historical ETL
197
IV.3.7 Summary and Conclusions
198
IV.4 Monte Carlo VaR
201
IV.4.1 Introduction
201
IV.4.2 Basic Concepts
203
IV.4.2.1 Pseudo-Random Number Generation
203
IV.4.2.2 Low Discrepancy Sequences
204
IV.4.2.3 Variance Reduction
206
IV.4
.2.4
Sampling from Univariate Distributions
211
IV.4.2.5 Sampling from Multivariate Distributions
213
IV.4.2.6 Introduction to Monte Carlo VaR
213
IV.4.3 Modelling Dynamic Properties in Risk Factor Returns
215
IV.4.3.1 Multi-Step Monte Carlo
215
IV.4.3.2 Volatility Clustering and Mean Reversion
218
IV.4.3.
3
Regime Switching Models
223
IV.4.4 Modelling Risk Factor Dependence
225
IV.4.4.1 Multivariate Distributions for i.i.d. Returns
226
IV.4.4.2 Principal Component Analysis
230
IV.4.4.3 Behavioural Models
232
IV.4.4.4 Case Study: Modelling the Price
-
Volatility
Relationship
232
IV.4.5 Monte Carlo Value at Risk for Linear Portfolios
233
IV.4.5.
1
Algorithms for VaR and ETL
235
IV.4.5.2 Cash-Flow Portfolios: Copula VaR and PC VaR
236
IV.4.5.3 Equity Portfolios: Crash Scenario VaR
239
IV.4.5.4 Currency Portfolios: VaR with Volatility Clustering
241
IV.4.6 Summary and Conclusions
244
IV.5 Value at Risk for Option Portfolios
247
IV.5.1 Introduction
247
IV.5.2 Risk Characteristics of Option Portfolios
250
IV.5.2.1 Gamma Effects
250
IV.5.2.2 Delta and
Vega
Effects
252
IV.5.2.3 Theta and Rho Effects
253
IV.5.2.4 Static and Dynamic VaR Estimates
254
IV.5.3 Analytic Value-at-Risk Approximations
257
IV.5.3
.1
Delta Approximation and Delta-Normal VaR
257
IV.5.3.2 P&L Distributions for Option Portfolios
259
IV.5.3.3 Delta-Gamma VaR
260
Contents xi
1У.5Л
Historical Value at Risk for Option Portfolios
262
IV.5
.4.1
VaR and ETL with Exact Revaluation
263
rv.5.4.2 Dynamically Hedged Option Portfolios
272
IV.5.4.3 Greeks Approximation
273
IV.5.
4.4
Historical VaR for Path-Dependent Options
278
IV.5.4.5 Case Study: Historical VaR for an Energy Options
Trading Book
280
IV.5
.5
Monte Carlo Value at Risk for Option Portfolios
282
IV.5.5.
1
Monte Carlo VaR and ETL with Exact Revaluation
283
IV.5.5.2 Risk Factor Models for Simulating Options VaR
287
IV.5.
5.3
Capturing Non-normality and Non-linearity
287
rv.5.5.4 Capturing Gamma,
Vega
and Theta Effects
290
IV.5.5.5 Path Dependency
292
IV.5
.5.6
Option Portfolios with a Single Underlying
296
IV.5.5.7 Option Portfolios with Several Underlyings
299
IV.5.5.8 Case Study: Monte Carlo VaR for an Energy Options
Trading Book
302
IV.5.6 Summary and Conclusions
307
IV.6 Risk Model Risk
311
IV.6.1 Introduction
311
IV.6.2 Sources of Risk Model Risk
313
IV.6.2.
1
Risk Factor Mapping
314
IV.6.2.2 Risk Factor or Asset Returns Model
319
IV.6.2.3 VaR Resolution Method
322
IV.6.2.4 Scaling
323
IV.6.3 Estimation Risk
324
IV.6.3.1 Distribution of VaR Estimators in Parametric Linear
Models
324
IV.6.3.2 Distribution of VaR Estimators in Simulation Models
328
IV.6.4 Model Validation
332
IV.6.4.1 Backtesting Methodology
332
IV.6.4.2 Guidelines for Backtesting from Banking Regulators
335
IV.6.4.3 Coverage Tests
337
IV.6.4.4
Backtests
Based on Regression
340
rv.6.4.5 Backtesting ETL Forecasts
344
rV.6.4.6 Bias Statistics for Normal Linear VaR
345
JV.6A.7 Distribution Forecasts
348
IV.6.4.8 Some Backtesting Results
351
FV.6.5 Summary and Conclusions
353
rv.7 Scenario Analysis and Stress Testing
357
IV.7.1 Introduction 357
IV.7.2 Scenarios on Financial Risk Factors
359
IV.7.2.
1
Broad Categorization of Scenarios
360
IV.7.2.2 Historical Scenarios
361
IV.7.2.3 Hypothetical Scenarios
362
rv.7.2.4 Distribution Scenario Design
366
Contents
IV.7.3
Scenario
Value at Risk and Expected Tail Loss
367
IV.7.3.1 Normal Distribution Scenarios
367
IV.7.3.2 Compound Distribution Scenario VaR
371
IV.7.3.3 Bayesian VaR
375
IV.7.4 Introduction to Stress Testing
378
IV.7.4.1 Regulatory Guidelines
379
IV.7.4.2 Systemic Risk
381
IV.7.4.3 Stress Tests Based on Worst Case Loss
381
1V.7.5 A Coherent Framework for Stress Testing
384
IV.7.5.
1
VaR Based on Stressed Covariance Matrices
385
IV.7.5.2 Generating Hypothetical Covariance Matrices
388
IV.7.5.3 Stress Tests Based on Principal Component Analysis
390
IV.7.5.4 Modelling Liquidity Risk
392
IV.7.5.5 Incorporating Volatility Clustering
397
IV.7.6 Summary and Conclusions
398
IV.8 Capital Allocation
401
IV.8.1 Introduction
401
IV.8.2 Minimum Market Risk Capital Requirements for Banks
403
IV.8.2.1 Basel Accords
404
IV.8.2.2 Banking and Trading Book Accounting
405
IV.8.2.3 Regulatory Framework for Market Risk
406
IV.8.2.4 Internal Models
408
IV.8.2.5 Standardized Rules
411
IV.8.2.6 Incremental Risk Charge
412
IV.8.3 Economic Capital Allocation
416
I V.8.3
.1
Measurement of Economic Capital
416
IV.8.3.2 Banking Applications of Economic Capital
421
IV.8.3.3 Aggregation Risk
422
IV.8.3.4 Risk Adjusted Performance Measures
424
IV.8.3.5 Optimal Allocation of Economic Capital
430
IV.8.4 Summary and Conclusions
433
References
Index
437
441
|
| adam_txt |
Contents
List of
Figures
xiii
List of Tables
xvi
List of Examples
xxi
Foreword
xxv
Preface to Volume IV
xxix
IV.l Value at Risk and Other Risk Metrics
1
IV.
1.1
Introduction
1
IV.
1.2
An Overview of Market Risk Assessment
4
IV.
1.2.1
Risk Measurement in Banks
4
IV.
1.2.2
Risk Measurement in Portfolio Management
6
IV.
1.2.3
Risk Measurement in Large Corporations
7
IV.
1.3
Downside and Quantile Risk Metrics
9
IV.
1.3.1
Semi-Standard Deviation and Second Order Lower
Partial Moment
9
TVÄ.
3.2
Other Lower Partial Moments
10
IV.
1.3.3
Quantile Risk Metrics
П
IV.
1.4
Defining Value at Risk
1
3
IV.
1.4.1
Confidence Level and Risk Horizon
13
IV.l.
4.2
Discounted P&L 15
IV.
1.4.3
Mathematical Definition of VaR
15
IV.
1.5
Foundations of Value-at-Risk Measurement
17
IV.l.
5.1
Normal Linear VaR Formula: Portfolio Level
18
IV.
1.5.2
Static Portfolios 20
IV.1.5.3
Scaling VaR 21
IV.
1.5.4
Discounting and the Expected Return
23
IV.
1.6
Risk Factor Value at Risk 25
IV.
1.6.1
Motivation 26
IV.
1.6.2
Normal Linear Equity VaR 27
IV.
1.6.3
Normal Linear Interest Rate VaR 29
Vlil
Contents
IV.
1.7
Decomposition of Value at Risk
30
IV.
1.7.1
Systematic and Specific VaR
31
IV.
1.7.2
Stand-alone VaR
31
IV.
1.7.3
Marginal and Incremental VaR
32
IV.
1.8
Risk Metrics Associated with Value at Risk
33
IV.
1.8.1
Benchmark VaR
34
IV.
1.8.2
Conditional VaR: Expected Tail Loss and Expected
Shortfall
35
IV.
1.8.3
Coherent Risk Metrics
38
IV.
1.9
Introduction to Value-at-Risk Models
41
IV.1.9.1 Normal Linear VaR
41
IV.
1.9.2
Historical Simulation
42
IV.
1.9.3
Monte Carlo Simulation
44
IV.
1.9.4
Case Study: VaR of the S&P
500
Index
45
I V.I
.10
Summary and Conclusions
47
IV.2 Parametric Linear VaR Models
53
IV.2.1 Introduction
53
IV.2.2 Foundations of Normal Linear Value at Risk
56
IV.2.2.
1
Understanding the Normal Linear VaR Formula
56
IV.2.2.2 Analytic Formula for Normal VaR when Returns are
Autocorrelated
60
IV.2.2.3 Systematic Normal Linear VaR
63
IV.2.2.4 Stand-Alone Normal Linear VaR
64
IV.2.2.5 Marginal and Incremental Normal Linear VaR
66
IV.2.3 Normal Linear Value at Risk for Cash-Flow Maps
67
IV.2.3.
1
Normal Linear Interest Rate VaR
67
IV.2.3.2 Calculating PV01
68
IV.2.3.3 Approximating Marginal and Incremental VaR
70
IV.2.3.4 Disaggregating Normal Linear Interest Rate VaR
72
IV.2.3.5 Normal Linear Credit Spread VaR
75
IV.2.4 Case Study: PC Value at Risk of a UK Fixed Income Portfolio
79
IV.2.4.
1
Calculating the Volatility and VaR of the Portfolio
80
IV.2.4.2 Combining Cash-Flow Mapping with PC A
81
IV.2.4.3 Advantages of Using PC Factors for Interest Rate VaR
85
IV.2.5 Normal Linear Value at Risk for Stock Portfolios
85
IV.2.5.
1
Cash Positions on a Few Stocks
86
IV.2.5.2 Systematic and Specific VaR for Domestic Stock
Portfolios
87
IV.2.5.3 Empirical Estimation of Specific VaR
90
IV.2.5.4 EWMA Estimates of Specific VaR
91
IV.2.6 Systematic Value-at-Risk Decomposition for Stock Portfolios
93
IV.2.6.
1
Portfolios Exposed to One Foreign Currency
93
IV.2.6.2 Portfolios Exposed to Several Foreign Currencies
97
I V.2.6.3 Interest Rate VaR of Equity Portfolios
100
IV.2.6.4 Hedging the Risks of International Equity Portfolios
101
IV.2.7 Case Study: Normal Linear Value at Risk for Commodity Futures
103
Contents
IV.2.8 Student
t
Distributed
Linear
Value at Risk
106
IV.2.8.1 Effect ofLeptokurtosis and Skewness on VaR
106
IV.2.8.2 Student
t
Linear VaR Formula
107
IV.2.8.3 Empirical Examples of Student
t
Linear VaR
109
IV.2.9 Linear Value at Risk with Mixture Distributions 111
IV.2.9.
1
Mixture Distributions
111
IV.2.9.2 Mixture Linear VaR Formula
113
IV.2.9.3 Mixture Parameter Estimation
114
IV.2.9.4 Examples of Mixture Linear VaR
115
IV.2.9.5 Normal Mixture Risk Factor VaR
119
IV.2.
10
Exponential Weighting with Parametric Linear Value at Risk
121
IV.2.10.1 Exponentially Weighted Moving Averages
121
IV.2.10.2 EWMA VaR at the Portfolio Level
124
IV.2.
10.3
RiskMetrics™ VaR Methodology
126
IV.2.
11
Expected Tail Loss (Conditional VaR)
128
IV.2.
11.1
ETL in the Normal Linear VaR Model
129
IV.2.11.2 ETL in the Student
t
Linear VaR Model
130
IV.2.
11.3
ETL in the Normal Mixture Linear VaR Model
132
IV.2.
11.4
ETL under a Mixture of Student
t
Distributions
133
IV.2.
12
Case Study: Credit Spread Parametric Linear Value at Risk and ETL
135
IV.2.12.1 The iTraxx Europe Index
135
IV.2.
12.2
VaR Estimates
137
IV.2.13 Summary and Conclusions
138
IV.3 ffistorical Simulation
141
IV.3.1 Introduction
141
IV.3.2 Properties of Historical Value at Risk
144
IV.3.2.1 Definition of Historical VaR
144
IV.3.2.2 Sample Size and Data Frequency
145
IV.3.2.3 Power Law Scale Exponents
146
IV.3.2.4 Case Study: Scale Exponents for Major Risk Factors
147
IV.3.2.5 Scaling Historical VaR for Linear Portfolios
150
IV.3.2.6 Errors from Square-Root Scaling of Historical VaR
151
IV.3.2.7 Overlapping Data and Multi-Step Historical Simulation
151
IV.3.3 Improving the Accuracy of Historical Value at Risk
152
IV.3.3.1 Case Study: Equally Weighted Historical and Linear VaR
153
IV.3.3.2 Exponential Weighting of Return Distributions
156
IV.3.3.3 Volatility Adjustment
158
IV.3.3.4 Filtered Historical Simulation
163
IV.3.4 Precision of Historical Value at Risk at Extreme Quantiles
165
IV.3.4.1 Kernel Fitting
165
IV.3.
4.2
Extreme Value Distributions
167
IV.3.4.3 Cornish-Fisher Approximation
170
IV.3.4.4 Johnson Distributions
172
IV.3
.5
Historical Value at Risk for Linear Portfolios
175
rv.3.5.1 Historical VaR for Cash Flows
176
rv.3.5.2 Total, Systematic and Specific VaR of a Stock Portfolio
179
Contents
IV.3.5.3
Equity and Forex VaR of an International Stock Portfolio
185
IV.3.5.4 Interest Rate and Forex VaR of an International Bond
Position
190
IV.3.5.5 Case Study: Historical VaR for a Crack Spread Trader
192
IV.3.6 Estimating Expected Tail Loss in the Historical Value-at-Risk Model
195
IV.3.6.1 Parametric Historical ETL
195
IV.3.6.2 Empirical Results on Historical ETL
195
IV.3.6.3 Disaggregation of Historical ETL
197
IV.3.7 Summary and Conclusions
198
IV.4 Monte Carlo VaR
201
IV.4.1 Introduction
201
IV.4.2 Basic Concepts
203
IV.4.2.1 Pseudo-Random Number Generation
203
IV.4.2.2 Low Discrepancy Sequences
204
IV.4.2.3 Variance Reduction
206
IV.4
.2.4
Sampling from Univariate Distributions
211
IV.4.2.5 Sampling from Multivariate Distributions
213
IV.4.2.6 Introduction to Monte Carlo VaR
213
IV.4.3 Modelling Dynamic Properties in Risk Factor Returns
215
IV.4.3.1 Multi-Step Monte Carlo
215
IV.4.3.2 Volatility Clustering and Mean Reversion
218
IV.4.3.
3
Regime Switching Models
223
IV.4.4 Modelling Risk Factor Dependence
225
IV.4.4.1 Multivariate Distributions for i.i.d. Returns
226
IV.4.4.2 Principal Component Analysis
230
IV.4.4.3 Behavioural Models
232
IV.4.4.4 Case Study: Modelling the Price
-
Volatility
Relationship
232
IV.4.5 Monte Carlo Value at Risk for Linear Portfolios
233
IV.4.5.
1
Algorithms for VaR and ETL
235
IV.4.5.2 Cash-Flow Portfolios: Copula VaR and PC VaR
236
IV.4.5.3 Equity Portfolios: 'Crash' Scenario VaR
239
IV.4.5.4 Currency Portfolios: VaR with Volatility Clustering
241
IV.4.6 Summary and Conclusions
244
IV.5 Value at Risk for Option Portfolios
247
IV.5.1 Introduction
247
IV.5.2 Risk Characteristics of Option Portfolios
250
IV.5.2.1 Gamma Effects
250
IV.5.2.2 Delta and
Vega
Effects
252
IV.5.2.3 Theta and Rho Effects
253
IV.5.2.4 Static and Dynamic VaR Estimates
254
IV.5.3 Analytic Value-at-Risk Approximations
257
IV.5.3
.1
Delta Approximation and Delta-Normal VaR
257
IV.5.3.2 P&L Distributions for Option Portfolios
259
IV.5.3.3 Delta-Gamma VaR
260
Contents xi
1У.5Л
Historical Value at Risk for Option Portfolios
262
IV.5
.4.1
VaR and ETL with Exact Revaluation
263
rv.5.4.2 Dynamically Hedged Option Portfolios
272
IV.5.4.3 Greeks Approximation
273
IV.5.
4.4
Historical VaR for Path-Dependent Options
278
IV.5.4.5 Case Study: Historical VaR for an Energy Options
Trading Book
280
IV.5
.5
Monte Carlo Value at Risk for Option Portfolios
282
IV.5.5.
1
Monte Carlo VaR and ETL with Exact Revaluation
283
IV.5.5.2 Risk Factor Models for Simulating Options VaR
287
IV.5.
5.3
Capturing Non-normality and Non-linearity
287
rv.5.5.4 Capturing Gamma,
Vega
and Theta Effects
290
IV.5.5.5 Path Dependency
292
IV.5
.5.6
Option Portfolios with a Single Underlying
296
IV.5.5.7 Option Portfolios with Several Underlyings
299
IV.5.5.8 Case Study: Monte Carlo VaR for an Energy Options
Trading Book
302
IV.5.6 Summary and Conclusions
307
IV.6 Risk Model Risk
311
IV.6.1 Introduction
311
IV.6.2 Sources of Risk Model Risk
313
IV.6.2.
1
Risk Factor Mapping
314
IV.6.2.2 Risk Factor or Asset Returns Model
319
IV.6.2.3 VaR Resolution Method
322
IV.6.2.4 Scaling
323
IV.6.3 Estimation Risk
324
IV.6.3.1 Distribution of VaR Estimators in Parametric Linear
Models
324
IV.6.3.2 Distribution of VaR Estimators in Simulation Models
328
IV.6.4 Model Validation
332
IV.6.4.1 Backtesting Methodology
332
IV.6.4.2 Guidelines for Backtesting from Banking Regulators
335
IV.6.4.3 Coverage Tests
337
IV.6.4.4
Backtests
Based on Regression
340
rv.6.4.5 Backtesting ETL Forecasts
344
rV.6.4.6 Bias Statistics for Normal Linear VaR
345
JV.6A.7 Distribution Forecasts
348
IV.6.4.8 Some Backtesting Results
351
FV.6.5 Summary and Conclusions
353
rv.7 Scenario Analysis and Stress Testing
357
IV.7.1 Introduction 357
IV.7.2 Scenarios on Financial Risk Factors
359
IV.7.2.
1
Broad Categorization of Scenarios
360
IV.7.2.2 Historical Scenarios
361
IV.7.2.3 Hypothetical Scenarios
362
rv.7.2.4 Distribution Scenario Design
366
Contents
IV.7.3
Scenario
Value at Risk and Expected Tail Loss
367
IV.7.3.1 Normal Distribution Scenarios
367
IV.7.3.2 Compound Distribution Scenario VaR
371
IV.7.3.3 Bayesian VaR
375
IV.7.4 Introduction to Stress Testing
378
IV.7.4.1 Regulatory Guidelines
379
IV.7.4.2 Systemic Risk
381
IV.7.4.3 Stress Tests Based on Worst Case Loss
381
1V.7.5 A Coherent Framework for Stress Testing
384
IV.7.5.
1
VaR Based on Stressed Covariance Matrices
385
IV.7.5.2 Generating Hypothetical Covariance Matrices
388
IV.7.5.3 Stress Tests Based on Principal Component Analysis
390
IV.7.5.4 Modelling Liquidity Risk
392
IV.7.5.5 Incorporating Volatility Clustering
397
IV.7.6 Summary and Conclusions
398
IV.8 Capital Allocation
401
IV.8.1 Introduction
401
IV.8.2 Minimum Market Risk Capital Requirements for Banks
403
IV.8.2.1 Basel Accords
404
IV.8.2.2 Banking and Trading Book Accounting
405
IV.8.2.3 Regulatory Framework for Market Risk
406
IV.8.2.4 Internal Models
408
IV.8.2.5 Standardized Rules
411
IV.8.2.6 Incremental Risk Charge
412
IV.8.3 Economic Capital Allocation
416
I V.8.3
.1
Measurement of Economic Capital
416
IV.8.3.2 Banking Applications of Economic Capital
421
IV.8.3.3 Aggregation Risk
422
IV.8.3.4 Risk Adjusted Performance Measures
424
IV.8.3.5 Optimal Allocation of Economic Capital
430
IV.8.4 Summary and Conclusions
433
References
Index
437
441 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T20:44:40Z |
| indexdate | 2024-07-09T21:15:12Z |
| institution | BVB |
| isbn | 9780470997888 |
| language | English |
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| spelling | Alexander, Carol Verfasser aut Market risk analysis 4 Value-at-risk models Carol Alexander Chichester [u.a.] Wiley 2008 XLII, 449 S. graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke (DE-604)BV023295503 4 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016480080&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Alexander, Carol Market risk analysis |
| title | Market risk analysis |
| title_auth | Market risk analysis |
| title_exact_search | Market risk analysis |
| title_exact_search_txtP | Market risk analysis |
| title_full | Market risk analysis 4 Value-at-risk models Carol Alexander |
| title_fullStr | Market risk analysis 4 Value-at-risk models Carol Alexander |
| title_full_unstemmed | Market risk analysis 4 Value-at-risk models Carol Alexander |
| title_short | Market risk analysis |
| title_sort | market risk analysis value at risk models |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016480080&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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