Table Of Content
Table of Contents
Series page
Title Page
Copyright
Preface
About this book
Whom is this book for?
Outline of the book
Acknowledgments
Chapter 1: Introduction
Banks and Risk Management
Evolution of Bank Capital Regulation
Creating Value from Risk Management
Financial Risk Systems
Model Risk Management
Part One: Market Risk
Chapter 2: Market Risk with the Normal Distribution
Linear Portfolios
Quadratic Portfolios
Simulation-Based Valuation
Chapter 3: Advanced Market Risk Analysis
Risk Measures, Risk Contributions, and Risk Information
Modeling the Stylized Facts of Financial Time Series
Time Scaling VaR and VaR with Trading
Market Liquidity Risk
Scenario Analysis and Stress Testing
Portfolio Optimization
Developments in the Market Risk Internal Models Capital Regulation
Part Two: Credit Risk
Chapter 4: Portfolio Credit Risk
Issuer Credit Risk in Wholesale Exposures and Trading Book
Credit Models for the Banking Book
Firmwide Portfolio Credit Risk and Credit Risk Dependence
Credit Risk Stress Testing
Features of New Generation Portfolio Credit Risk Models
Hedging Credit Risk
Regulatory Capital for Credit Risk
Appendix
Chapter 5: Counterparty Credit Risk
Counterparty Pricing and Exposure
CVA Risks
Portfolios of Derivatives
Recent Counterparty Credit Risk Developments
Counterparty Credit Risk Regulation
Part Three: Asset and Liability Management
Chapter 6: Liquidity Risk Management with Cash Flow Models
Measurement of Liquidity Risk
Liquidity Exposure
Hedging the Liquidity Exposure
Structural Liquidity Planning
Components of the Liquidity Hedging Program
Cash Liquidity Risk and Liquidity Risk Measures
Regulation for Liquidity Risk
Chapter 7: Funds Transfer Pricing and Profitability of Cash Flows
Basic Funds Transfer Pricing Concept
Risk-Based Funds Transfer Pricing
Funds Transfer Rate and Risk Adjusted Returns
Profitability Measures and Decompositions
Banking Book Fair Value with Funds Transfer Rates
A Note on the Scope of Funds Transfer Pricing
Regulation and Profitability Analysis
Part Four: Firmwide Risk
Chapter 8: Firmwide Risk Aggregation
Correlated Aggregation and Firmwide Risk Levels
Mixed Copula Aggregation
Capital Allocation in Risk Aggregation
Risk Aggregation and Regulation
Chapter 9: Firmwide Scenario Analysis and Stress Testing
Firmwide Scenario Model Approaches
Firmwide Risk Capital Measures
Regulatory Stress Scenario Approach
The Future of Firmwide Stress Testing
References
Index
End User License Agreement
List of Illustrations
Chapter 1: Introduction
Figure 1.1 Risk Calculation Flow in a Financial Risk System
Chapter 2: Market Risk with the Normal Distribution
Figure 2.1 Profit-and-Loss Profiles for Barrier Options for a Grid of the Underlying
Stock Value
Figure 2.2 100 Normal Simulated Points from a Pseudo-Random Number Generator
(Left) and a Quasi-Random Number Generator (Right)
Figure 2.3 The Inverse Function Transformation for the Normal Distribution
Figure 2.4 Eigenvalues and Variance Explained by Principal Components Analysis of
the US Treasury Curve
Figure 2.5 First Three Principal Components of the US Treasury Yield Curve
Chapter 3: Advanced Market Risk Analysis
Figure 3.1 VaR 99% Confidence Level Risk Measures, Incremental Risk, and Risk
Contributions for the Portfolio Instruments
Figure 3.2 Portfolio Trade Risk Profile for the European Call Option on Stock A as We
Vary Its Holding from 1 to −1
Figure 3.3 Trade Risk Profile for Convex and Non-convex Risk Measures
Figure 3.4 Empirical Distribution Function (CDF) and Block Maxima Distortion
Function for n Equal to 5, 10, and 20 for a Loss Sample
Figure 3.5 A Typical Financial Time Series of Returns that Displays the Well-Known
Property of Volatility Clustering
Figure 3.6 Autocorrelation of Returns and Squared Returns for the S&P 500 Index
Figure 3.7 GARCH Filtered Lower Tail Residuals of the USD/SEK Exchange Rate.
The Fitted Tail Distributions are the Empirical Distribution Function, Normal Density,
t-Density, and the Generalized Pareto Distribution
Figure 3.8 GARCH Filtered Lower Tail Residuals of the ABB Stock. The Fitted Tail
Distributions are the Empirical Distribution Function, Normal Density, t-Density, and
the Generalized Pareto Distribution
Figure 3.9 Bivariate Frechet Bound and Independence Copulas
Figure 3.10 Finite Tail Dependence for the Normal and t-Copula for Different Values
of the Correlation Parameter and Threshold
Figure 3.11 Bivariate Scatter Plots of Equity Returns
Figure 3.12 Bivariate Scatter Plots of 10,000 Uniform Copula Simulations of Returns
for Equity 1 and and Equity 2 from the Normal Copula, the t-Copula (Estimated with
Kendall's Tau), and Archimedean Copulas Estimated with Kendall's Tau (Clayton and
Frank)
Figure 3.13 Bivariate Scatter Plots of 10,000 Empirical Density Copula Simulations of
Returns for Equity 1 and Equity 2 from the Normal Copula, the t-Copula (Estimated
with Kendall's Tau), and Archimedean Copulas Estimated with Kendall's Tau (Clayton
and Frank)
Figure 3.14 VaR at the 99% Confidence Level for Partial and Full Closeout at the
Liquidity Horizons
Figure 3.15 VaR at the 99% Confidence Level for Full Closeout for Different Stocks at
the Liquidity Horizons and Full Closeout at the Liquidity Horizons
Figure 3.16 Index Portfolio Returns Between May 3, 1993, and December 26, 2011
Figure 3.17 Conditional Mean, Most Likely Loss and 50% and 90% Confidence
Intervals Around the Points for the Nikkei 225 and Hang Seng Index Risk Factors
Figure 3.18 Efficient Frontiers for the Unconstrained and the Constrained Case Across
CVaR 99% Confidence Risk Ranging Between 1 and 15% of Portfolio Mark to Market
Figure 3.19 Asset 1 and Liability Cash Flow Scenarios for the 8 Time Buckets
Chapter 4: Portfolio Credit Risk
Figure 4.1 Merton Credit Spreads in Percent as the Debt Ratio, K/V, Varies Between
50, 65, and 75% and for 1, …, 10 Years Bond Maturity
Figure 4.2 Example of Obtained Rating Grade Thresholds Using the Transition
Probabilities of the Standard and Poor's Rating Grade Scale
Figure 4.3 Corporate Bond Portfolio VaR at Different Confidence Levels
Figure 4.4 Firm Portfolio VaR at Horizons 3, 6, 9, and 12 Months
Figure 4.5 Credit Portfolio Loss Tail for the Normal and t(3) Copula for Confidence
Levels 99% and Higher
Figure 4.6 Mixed Firm and Pool Portfolio VaR and CVaR Risk Measures at the 12-
Month Horizon
Figure 4.7 99.9% VaR (Expressed in Percentage of Current Mark to Market) for the
Firms Together with the 95% Lower and Upper Confidence Levels for the Different
Simulation Sizes
Figure 4.8 99.9% VaR (Expressed in Percentage of Current Mark to Market) for the
Pools Together with the 95% Lower and Upper Confidence Levels for the Different
Simulation Sizes
Figure 4.9 Simulation Scatterplot of Default Times (Expressed in Years) from a
Normal Copula with Correlation Parameter 0 Using 100,000 Simulations
Figure 4.10 Simulation Scatterplot of Default Times (Expressed in Years) from a
Normal Copula with Correlation Parameter 0.99 Using 100,000 Simulations
Figure 4.11 Simulation Scatterplot of Default Times (Expressed in Years) from a
Clayton Copula with Copula Parameter 30 Using 100,000 Simulations
Figure 4.12 Historical Data for the Systematic Factor and the Price Indices
Figure 4.13 Aggregate Portfolio Marginal Risk and Expected Loss at Horizons of 1, …,
10 Years
Figure 4.14 99.9% VaR for the Credit Losses for the Large Pool Subportfolios 10, 11,
and 14
Figure 4.15 99.9% VaR for the Credit Losses for the Large Pool Subportfolios 1, 3, and
6
Figure 4.16 99.9% VaR for the Net Credit Losses, Credit Losses, and the Expected
Loss Adjusted Credit Losses for the Aggregate Portfolio
Figure 4.17 Regulatory Capital 99.9% VaR and Expected Value over the Risk Horizon
of 1, …, 10 Years for the Aggregate Portfolio
Figure 4.18 Regulatory Capital 99.9% VaR and Expected Value over the Risk Horizon
of 1, …, 10 Years for Subportfolio 11 in Grade 2
Figure 4.19 Aggregate Portfolio Percent Increase of Marginal Risk for 1, …, 10 Years
Using Sampling for all the Portfolio Loans
Figure 4.20 Subportfolio 8 Percent Increase of Marginal Risk for 1, …, 10 Years Using
Sampling for all the Portfolio Loans
Figure 4.21 Subportfolio 10 and 14 Percent Increase of Marginal Risk for 1, …, 10
Years Using Sampling for all the Portfolio Loans
Figure 4.22 Loss Probability Density Obtained from the Adjusted Panjer Recursion
When Average Loan Default Rates Are Reduced by a Factor of 10 and When the
Average Deafult Rates Are Unadjusted
Figure 4.23 Pools Portfolio Loss in Each Scenario
Figure 4.24 Systematic Risk Factor Scenarios in the Extreme and Moderate Economic
Distress Cases
Figure 4.25 Aggregate Mortgage Portfolio Scenario Analysis of Net Earnings and
Regulatory Capital
Figure 4.26 Mortgage Portfolio Subportfolio 11 in Rating Class 2 Scenario Analysis of
Net Earnings and Regulatory Capital
Figure 4.27 Potential Recovery Process
Figure 4.28 Credit Model with Cash Flows
Figure 4.29 Sample Survival Curves A, B, and C
Chapter 5: Counterparty Credit Risk
Figure 5.1 Obtaining Default Probabilities of Counterparties
Figure 5.2 Market Zero Rate and Instantaneous Forward Rate Term Structure
Figure 5.3 Sample Simulation Paths for the Calibrated Hull-White Model
Figure 5.4 10,000 Simulated Market Trajectories for the 1-Year Term Node Interest
Rate on Days 1, …, 2600
Figure 5.5 10,000 Simulated Market Trajectories for the FX Forward Rate on Days 1,
…, 2600
Figure 5.6 Expected Exposure, the Running Mean of Expected Positive Exposures, and
the Peak Exposure Profile for a 10-Year at-the-Money Payer Swap
Figure 5.7 Expected Exposure, the Running Mean of Expected Positive Exposures, and
the Peak Exposure Profile for a 10-Year In-the-Money Payer Swap
Figure 5.8 Expected Exposure, the Running Mean of Expected Positive Exposures, and
the Peak Exposure Profile for a 10-Year Out-of-the-Money Payer Swap
Figure 5.9 Expected Exposure, the Running Mean of Expected Positive Exposures, and
the Peak Exposure Profile for a 10-Year at-the-Money Receiver Swap
Figure 5.10 Comparison of Expected Exposure for 10-Year at-the-Money Receiver and
Payer Swaps
Figure 5.11 Expected Exposure, the Running Mean of Expected Positive Exposures,
and the Peak Exposure Profile for a 10-Year at-the-Money Cross Currency Payer Swap
Figure 5.12 Expected Exposure, the Running Mean of Expected Positive Exposures,
and the Peak Exposure Profile for a 10-Year at-the-Money Payer Swap with Unequal
Payment Frequencies—Pay Quarterly and Receive Yearly
Figure 5.13 Expected Exposure, the Running Mean of Expected Positive Exposures,
and the Peak Exposure Profile for a 10-Year at-the-Money Payer Swap with Unequal
Payment Frequencies—Pay Yearly and Receive Quarterly
Figure 5.14 Sample Collateral Flows for a 1-Year at-the-Money Interest Rate Swap
Exposure Path
Figure 5.15 Expected Exposure, the Running Mean of Expected Positive Exposures,
and the Peak Exposure Profile for a 1-Year at-the-Money Payer Swap With No
Collateral
Figure 5.16 Expected Exposure, the Running Mean of Expected Positive Exposures,
and the Peak Exposure Profile for a 1-Year at-the-Money Payer Swap with Daily
Margin and No Settlement Risk
Figure 5.17 Expected Exposure, the Running Mean of Expected Positive Exposures,
and the Peak Exposure Profile for a 1-Year at-the-Money Payer Swap with Daily
Margin and 5-Day Settlement Risk
Figure 5.18 Expected Exposure, the Running Mean of Expected Positive Exposures,
and the Peak Exposure Profile for a 1-Year at-the-Money Payer Swap with Daily
Margin and 10-Day Settlement Risk
Figure 5.19 Expected Exposure for a 1-Year at-the-Money Payer Swap,
Uncollateralized and with Different Settlement Risks
Figure 5.20 Expected Exposure, the Running Mean of Expected Positive Exposures,
and the Peak Exposure Profile for a 1-Year at-the-Money Payer Swap with 10-Day
Margin Frequency and No Settlement Risk
Figure 5.21 Expected Exposure, the Running Mean of Expected Positive Exposures,
and the Peak Exposure Profile for a 1-Year at-the-Money Payer Swap with 10-Day
Margin Frequency and 5-Day Settlement Risk
Figure 5.22 Expected Exposure, the Running Mean of Expected Positive Exposures,
and the Peak Exposure Profile for a 1-Year at-the-Money Payer Swap with 10-Day
Margin Frequency and 10-Day Settlement Risk
Figure 5.23 Expected Exposures for Portfolio Trades and the Netted Portfolio
Figure 5.24 Peak Exposures for Portfolio Trades and the Netted Portfolio
Figure 5.25 Marginal Expected Exposures for Portfolio Trades and the Netted Portfolio
Figure 5.26 Marginal Worst-Case Exposures for Portfolio Trades and the Netted
Portfolio
Chapter 6: Liquidity Risk Management with Cash Flow Models
Figure 6.1 Sample Cash Flows, Forward Liquidity Exposures, and Risk Reserve
Process for Liquidity Scenario 1
Figure 6.2 Sample Cash Flows, Forward Liquidity Exposures, and Risk Reserve
Process for Liquidity Scenario 2
Figure 6.3 Cash Liquidity Needs for the 3 Liquidity Scenarios
Figure 6.4 Cash Liquidity Need for the 3 Liquidities, the Portfolio, and the Summed
Liquidity Need
Chapter 7: Funds Transfer Pricing and Profitability of Cash Flows
Figure 7.1 Funding Curve Used in Calculation of Funds Transfer Rates
Figure 7.2 FTP Breakdown of the Balance Sheet
Figure 7.3 Sample Mortgage Net Interest Margin Relative to Synthetic FTP Legs
Chapter 8: Firmwide Risk Aggregation
Figure 8.1 Sample Risk Aggregation Hierarchies
Chapter 9: Firmwide Scenario Analysis and Stress Testing
Figure 9.1 Firmwide Risk-Based Capital Stress Testing
Figure 9.2 Regulatory Stress Scenario Approach
Figure 9.3 Firmwide Stress Testing Process
List of Tables
Chapter 2: Market Risk with the Normal Distribution
Table 2.1 The VaR(0.99) and CVaR(0.99) Risk Measures for the Aggregate Portfolio
and the Equity Positions, P , …, P . The Table also Displays the VaR(0.99) and
1 5
CVaR(0.99) Euler Risk Contributions with Respect to the Positions P , …, P
1 5
Table 2.2 Profit-and-Loss Profiles for Barrier Options for a Grid of the Underlying
Stock Value
Table 2.3 Mean and Standard Deviation of US Treasury Historical Yields
Table 2.4 First Three Principal Components of the US Treasury Yield Curve
Chapter 3: Advanced Market Risk Analysis
Table 3.1 Sample Equity Portfolio
Table 3.2 Sample Equity Portfolio Risk Measures for 1,000, 10,000, 100,000, and
1,000,000 Scenarios
Table 3.3 Example Ordered Loss Matrix
Table 3.4 VaR and CVaR 99% Confidence Level Risk Measures, Incremental Risk, and
Risk Contributions for the Portfolio Instruments
Table 3.5 Portfolio Trade Risk Profile for the European Call Option on Stock A as we
Vary Its Holding from 1 to
Table 3.6 VaR Risk Contributions and Smoothed Risk Contributions for the Portfolio
Instruments
Table 3.7 VaR and CVaR 99% Confidence Level Diversification Indices
Table 3.8 Sample Distributions of X and Y (Bold Sample Numbers Indicate the Sample
Belonging to the Left Part of the Distribution, i.e., the First Quintile for s = 2)
Table 3.10 Risk Factor Information Measures and Correlation of Equity Risk Factors to
Portfolio Profit and Loss
Table 3.9 Risk Factor Information Measures and Correlation of Equity Risk Factors to
Portfolio Profit and Loss When Holding in Equity A is Changed to 10 Units Instead of 1
Unit
Table 3.11 Risk Distortion Measures
Table 3.12 Unconditional Moments of Returns to the SP 500 Index
Table 3.13 Hill-Based Exteme Value Portfolio Risk for Different Percentage Sample
Points in the Tail
Table 3.14 Sample Equity Returns for 10 Days
Table 3.15 Estimation of Theta Parameter for Archimedean Copulas Clayton, Gumbel,
and Frank Using Kendall's Tau and Maximum Likelihood Method
Table 3.16 VaR Exceedances for the Models
Table 3.17 Days Between VaR Exceedances for the Models
Table 3.18 VaR Backtesting Comparison of the Models, Comparing Expected Number
of Exceedances Versus Actual and p-Values from the Unconditional Coverage Test, the
Independence and the Duration Test
Table 3.19 Stock Allocation to Liquidity Groups
Table 3.20 Percent Closeout VaR Profile and the No-Closeout VaR Profile on Either of
Days 1, …, 15
Table 3.21 Stock Allocation to Full Closeout Horizons
Table 3.22 Percent Tiered Full Closeout VaR Profile on Days 1, …, 15
Table 3.23 Delta Approximation of 3 Market Risk Books
Table 3.24 Market Indices Volatility and Degrees of Freedom
Table 3.25 VaR and CVaR 99% Confidence Level Risk Measures, Incremental Risk,
and Risk Contributions for the Approximate Firmwide Market Risk Portfolio
