Advanced financial risk management

Advanced Financial
Risk Management


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Advanced Financial
Risk Management
Second Edition
Tools and Techniques for Integrated
Credit Risk and Interest Rate
Risk Management

DONALD R. VAN DEVENTER
KENJI IMAI
MARK MESLER


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ISBN

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For Yasuko, Tomoki, and Anna.
K. I.
To all of our colleagues at Kamakura.
M. M.
For Ayako, Ella, Ai, and Yuu.
D. v. D.



Contents

Introduction: Wall Street Lessons from Bubbles

Key Fallacies in Risk Management
Selected Events in the Credit Crisis

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PART ONE

Risk Management: Definitions and Objectives
CHAPTER 1
A Risk Management Synthesis: Market Risk, Credit Risk, Liquidity Risk,
and Asset and Liability Management
Risk Management: Definitions and Objectives
Advances in Integrated Risk Management and Institutional
Barriers to Progress
Measuring the Trade-Offs between Risk and Return
When Bad Things Happen to Good People
U.S. Savings and Loan Crisis
Long-Term Capital Management
The 2006À2011 Credit Crisis
A Thousand Cuts

CHAPTER 2
Risk, Return, Performance Measurement, and Capital Regulation
Practical Quantification of Risk
Perils and Pitfalls in the Measurement of Risk: The Impact
of Selection Bias
Biases in Return vs. a Relative Benchmark
Historical Value at Risk: Selection Bias Again

Monte CarloÀBased Value at Risk
Expected Losses on Tranches of Collateralized Debt Obligations
Measuring Return: Market vs. Accounting Returns
Introduction to Transfer Pricing: Extracting Interest Rate Risk
in a Financial Accounting Context
Bank of America, 1973À1979
First Interstate, 1982À1987
Performance Measurement and Capital Regulation
Perspectives on Measuring Risk: One Source of Risk or Many
Sources of Risk?
Interest Rate Risk Management Evolution
Equity Risk Management Evolution

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Option Risk Management Evolution
Credit Risk Management Evolution
Managing Risk and Strategy, Business by Business
Risk and Strategy Management in a Complex Financial Institution
What Causes Financial Institutions to Fail?
The Role of Capital in Risk Management and Business Strategy
Capital-Based Risk Management in Banking Today: Pros and Cons
History of Capital-Based Regulations in Commercial Banking

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PART TWO

Risk Management Techniques for Interest Rate Analytics
CHAPTER 3
Interest Rate Risk Introduction and Overview
Background Information on Movements in the U.S. Treasury
Yield Curve
A Step-by-Step Approach to Analyzing Interest Rate Risk
The Interest Rate Risk Safety Zone

CHAPTER 4
Fixed Income Mathematics: The Basic Tools
Modern Implications of Present Value
Price, Accrued Interest, and Value
Calculation of Accrued Interest
Present Value
The Basic Present Value Calculation
Example
Calculating the Value of a Fixed Coupon Bond with
Principal Paid at Maturity
Calculating the Coupon of a Fixed Coupon Bond with
Principal Paid at Maturity When the Value Is Known
Example
The Value of an Amortizing Loan
Calculating the Payment Amount of an Amortizing Bond
When the Value Is Known
Risk Management Implications

Calculating the Value of a Floating-Rate Bond or Loan with
Principal Paid at Maturity
Example
Risk Management Implications
Compound Interest Conventions and Formulas
Future Value of an Invested Amount Earning at a Simple Interest
Rate of y Compounded m Times per Year for n Periods
Future Value of an Invested Amount Earning at a Simple Interest
Rate of y Compounded Continuously for n Years
Example
Present Value of a Future Amount If Funds Are Invested at a
Simple Interest Rate of y Compounded m Times per
Year for n Periods

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Present Value of a Future Amount If Funds Are Invested at a Simple
Interest Rate of y Compounded Continuously for n Years
Compounding Formulas and Present Value Factors P(t)
Yields and Yield-to-Maturity Calculations
The Formula for Yield to Maturity
Yield to Maturity for Long or Short First Coupon Payment Periods
Calculating Forward Interest Rates and Bond Prices
Implied Forward Interest Rates on Zero-Coupon Bonds
Example
Implied Forward Zero-Coupon Bond Prices
Present Value of Forward Fixed Coupon Bond
Implied Forward Price on a Fixed Coupon Bond
Implied Forward Coupon on a Fixed Coupon Bond
Other Forward Calculations
Summary

CHAPTER 5
Yield Curve Smoothing
Example A: Stepwise Constant Yields and Forwards vs. Nelson-Siegel
Deriving the Form of the Yield Curve Implied by Example A
Fitting the Nelson-Siegel Approach to Sample Data
Example D: Quadratic Yield Splines and Related Forward Rates
Deriving the Form of the Yield Curve Implied by Example D
Example F: Cubic Yield Splines and Related Forwards
Deriving the Form of the Yield Curve Implied by
Example F Assumptions
Example H: Maximum Smoothness Forward
Rates and Related Yields
Deriving the Parameters of the Quartic Forward Rate Curves
Implied by Example H Assumptions
Comparing Yield Curve and Forward Rate Smoothing Techniques
Ranking 23 Smoothing Techniques by Smoothness of the
Forward Rate Curve
Ranking 23 Smoothing Techniques by Length of the
Forward Curve
Trading Off Smoothness vs. the Length of the Forward Rate Curve
The Shimko Test for Measuring Accuracy of Smoothing Techniques
Smoothing Yield Curves Using Coupon-Bearing Bond Prices as Inputs
Appendix: Proof of the Maximum Smoothness Forward Rate Theorem

CHAPTER 6
Introduction to Heath, Jarrow, and Morton Interest Rate Modeling
Objectives of the Example and Key Input Data
Key Implications and Notation of the HJM Approach
Pseudo-Probabilities

The Formula for Zero-Coupon Bond Price Shifts
Building the Bushy Tree for Zero-Coupon Bonds
Maturing at Time T 5 2

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Building the Bushy Tree for Zero-Coupon Bonds
Maturing at Time T 5 4
Valuation in the HJM Framework
Valuation of a Zero-Coupon Bond Maturing at Time T 5 4
Valuation of a Coupon-Bearing Bond Paying Annual Interest
Valuation of a Digital Option on the One-Year U.S. Treasury Rate
Conclusion

CHAPTER 7
HJM Interest Rate Modeling with Rate and Maturity-Dependent Volatility

Objectives of the Example and Key Input Data
Key Implications and Notation of the HJM Approach
Pseudo-Probabilities
The Formula for Zero-Coupon Bond Price Shifts
Building the Bushy Tree for Zero-Coupon Bonds
Maturing at Time T 5 2
Building the Bushy Tree for Zero-Coupon Bonds
Maturing at Time T 5 4
Valuation in the HJM Framework
Valuation of a Zero-Coupon Bond Maturing at Time T 5 4
Valuation of a Coupon-Bearing Bond Paying Annual Interest
Valuation of a Digital Option on the One-Year U.S. Treasury Rate
Conclusion

CHAPTER 8
HJM Interest Rate Modeling with Two Risk Factors
Probability of Yield Curve Twists in the U.S. Treasury Market
Objectives of the Example and Key Input Data
Introducing a Second Risk Factor Driving Interest Rates
Key Implications and Notation of the HJM Approach
Pseudo-Probabilities
The Formula for Zero-Coupon Bond Price Shifts with
Two Risk Factors
Building the Bushy Tree for Zero-Coupon Bonds
Maturing at Time T 5 2
Building the Bushy Tree for Zero-Coupon Bonds
Maturing at Time T 5 3
Building the Bushy Tree for Zero-Coupon Bonds
Maturing at Time T 5 4
Valuation in the HJM Framework

Valuation of a Zero-Coupon Bond Maturing at Time T 5 4
Valuation of a Coupon-Bearing Bond Paying Annual Interest
Valuation of a Digital Option on the One-Year
U.S. Treasury Rate
Replication of HJM Example 3 in Common Spreadsheet Software
Conclusion

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CHAPTER 9
HJM Interest Rate Modeling with Three Risk Factors
Probability of Yield Curve Twists in the U.S. Treasury Market
Objectives of the Example and Key Input Data
Risk Factor 1: Annual Changes in the One-Year U.S.
Treasury Spot Rate
Alternative Specifications of the Interest Rate Volatility Surface
Key Implications and Notation of the HJM Approach
Pseudo-Probabilities
The Formula for Zero-Coupon Bond Price Shifts with
Three Risk Factors
Building the Bushy Tree for Zero-Coupon Bonds
Maturing at Time T 5 2

Building the Bushy Tree for Zero-Coupon Bonds
Maturing at Time T 5 3
Building the Bushy Tree for Zero-Coupon Bonds
Maturing at Time T 5 4
Valuation in the HJM Framework
Valuation of a Zero-Coupon Bond Maturing at Time T 5 4
Valuation of a Coupon-Bearing Bond Paying Annual Interest
Valuation of a Digital Option on the One-Year
U.S. Treasury Rate
Conclusion

CHAPTER 10
Valuation, Liquidity, and Net Income
How Many Risk Factors Are Necessary to Accurately
Model Movements in the Risk-Free Yield Curve?
Revisiting the Phrase “No Arbitrage”
Valuation, Liquidity Risk, and Net Income
Risk-Neutral and Empirical Probabilities of Interest
Rate Movements
Monte Carlo Simulation Using HJM Modeling
Common Pitfalls in Interest Rate Risk Management
Pitfalls in the Use of One-Factor Term Structure Models
Common Pitfalls in Asset and Liability Management
Summarizing the Problems with Interpolated Monte Carlo
Simulation for Risk Analysis

CHAPTER 11
Interest Rate Mismatching and Hedging
Political Factions in Interest Rate Risk Management
Pension Fund Considerations

Life Insurance Companies and Property and Casualty Insurance
Companies
Commercial Banks

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Making a Decision on Interest Rate Risk and Return:
The Safety Zone
Obvious Interest Rate Risk Decisions
Assessing the Risk and Return Trade-Offs from a
Change in Interest Rate Risk

CHAPTER 12
Legacy Approaches to Interest Rate Risk Management
Gap Analysis and Simulation Models
Measuring Interest Rate Risk: A Review
Legacy Rate Risk Tools: Interest Rate Sensitivity Gap Analysis
The Safety Zone
What’s Wrong with Gap Analysis?
Legacy Rate Risk Tools: Multiperiod Simulation
Key Assumptions in Simulation
Data Aggregation in Simulation Modeling

Constraining the Model
Modeling the Maturity Structure of a Class of Assets
Periodicity of the Analysis
Exceptions to the Exact Day Count Trend
Legacy Rate Risk Tools: Duration and Convexity
Macaulay’s Duration: The Original Formula
Using Duration for Hedging
Comparing a Duration Hedge with Hedging in the HJM Framework
Duration: The Traditional Market Convention
The Formula for Yield to Maturity
Yield to Maturity for Long or Short First Coupon Payment Periods
Applying the Yield-to-Maturity Formula to Duration
Modified Duration
The Perfect Duration Hedge: The Difference between the
Original Macaulay and Conventional Durations
Convexity and Its Uses
Convexity: A General Definition
Convexity for the Present Value Formula
Hedging Implications of the Convexity Concept
Conclusion

CHAPTER 13
Special Cases of Heath, Jarrow, and Morton Interest Rate Modeling
What Is an Academic Term Structure Model and Why
Was It Developed?
The Vocabulary of Term Structure Models
Ito’s Lemma
Ito’s Lemma for More Than One Random Variable
Using Ito’s Lemma to Build a Term Structure Model
Duration as a Term Structure Model

Conclusions about the Use of Duration’s Parallel Shift Assumptions
The Vasicek and Extended Vasicek Models

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Contents

The Merton Term Structure Model: Parallel Yield Curve Shifts
The Extended Merton Model
The Vasicek Model
The Extended VasicekÀHull and White Model
Alternative Term Structure Models
Alternative One-Factor Interest Rate Models
Two-Factor Interest Rate Models
Chen’s Three-Factor Term Structure Model
Reprising the HJM Approach
Appendix A: Deriving Zero-Coupon Bond Prices in the
Extended Merton/Ho and Lee Model

Appendix B: Deriving Zero-Coupon Bond Prices in the
Vasicek Model
Appendix C: Valuing Zero-Coupon Bonds in the Extended
Vasicek Model

CHAPTER 14
Estimating the Parameters of Interest Rate Models
Revisiting the Meaning of No Arbitrage
A Framework for Fitting Term Structure Models
Fitting Zero-Coupon Bond Prices and Volatility Parameters Jointly
Steps in Fitting the Interest Rate Volatility Assumptions
Example 1: Fitting Interest Rate Volatility When
Six Callable Bonds Are Observable
Example 2: The Consequences of Fewer Inputs
Example 3: The Case of One Input
Interest Rate Parameter Fitting in Practical Application

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PART THREE

Risk Management Techniques for Credit Risk Analytics
CHAPTER 15
An Introduction to Credit Risk: Using Market Signals in Loan
Pricing and Performance Measurement
Market Prices for Credit Risk
Critical Sources of Market Data on Credit Risk
Bond Prices
Credit Default Swap Prices
First to Default Swaps
Collateralized Debt Obligations
Interest Rate Swap Prices
Equity Prices
Increased Accuracy in Pricing
Increased Clarity in Corporate Strategy
Increased Sophistication in Risk Management
Increased Precision in Measuring the Safety and
Soundness of Financial Institutions

Credit Default Swaps: The Dangers of Market Manipulation

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Daily Nondealer Trading Volume for 1,090 Reference Names
Credit Default Swap Trading Volume in Municipals and
Sub-Sovereigns
Credit Default Swap Trading Volume in Sovereign Credits
Implications of CDS Trading Volume Data

CHAPTER 16
Reduced Form Credit Models and Credit Model Testing
The Jarrow-Turnbull Model

The Jarrow-Turnbull Framework
The Jarrow Model
Zero-Coupon Bond Prices in the Jarrow Model
The Jarrow Model and the Issue of Liquidity in the Bond Market
The Jarrow-Merton Put Option as a Risk Index
and a Practical Hedge
Fitting the Jarrow Model to Bond Prices, Credit Derivatives
Prices, and Historical Default Databases
Fitting the Jarrow Model to Debt Prices
Fitting to Current Price Data and Historical Price Data
Fitting the Jarrow Model to Credit Derivatives Prices
Fitting the Jarrow Model to a Historical Database of Defaults
Fitting the Jarrow Model to Retail, Small Business, and
Governmental Counterparties
Correlations in Default Probabilities
The Jarrow and Jarrow-Turnbull Models: A Summary
Tests of Credit Models Using Historical Data
An Introduction to Credit Model Testing
Misunderstandings about Credit Model Testing
The Two Components of Credit Model Performance
Measuring Ordinal Ranking of Companies by Credit Risk
The Predictive ROC Accuracy Ratio: Techniques and Results
The Predictive Capability of the Jarrow-Chava Reduced
Form Model Default Probabilities
Measuring the Predictive ROC Accuracy Ratio
Reduced Form Model vs. Merton Model Performance
Consistency of Estimated and Actual Defaults
Recent Results from North America
The Falkenstein and Boral Test
Performance of Credit Models vs. Naïve Models of Risk

ROC Accuracy Ratios for Merton Model Theoretical
Version vs. Selected Naïve Models
Tests of Credit Models Using Market Data
Testing Credit Models: The Analogy with Interest Rates
Market Data Test 1: Accuracy in Fitting Observable
Yield Curves and Credit Spreads
Market Data Test 2: Tests of Hedging Performance
Market Data Test 3: Consistency of Model Implications
with Model Performance

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Market Data Test 4: Comparing Performance with Credit
Spreads and Credit Default Swap Prices
Appendix: Converting Default Intensities to Discrete
Default Probabilities
Converting Monthly Default Probabilities to Annual Default
Probabilities
Converting Annual Default Probabilities to Monthly Default

Probabilities
Converting Continuous Instantaneous Probabilities of
Default to an Annual Default Probability or Monthly
Default Probability
Converting Continuous Default Probability to an
Annual Default Probability
Converting Continuous Default Probability to a
Monthly Default Probability
Converting an Annual Default Probability to a Continuous
Default Intensity
Converting a Monthly Default Probability to a Continuous
Default Intensity

CHAPTER 17
Credit Spread Fitting and Modeling
Introduction to Credit Spread Smoothing
The Market Convention for Credit Spreads
A Better Convention for Credit ModelÀIndependent Credit Spreads
Deriving the Full Credit Spread of a Risky Issuer
Credit Spread Smoothing Using Yield CurveÀSmoothing Techniques
Setting the Scene: Smoothing Results for the Risk-Free Curve
A Naïve Approach: Smoothing ABC Yields by Ignoring
the Risk-Free Curve
Fitting Credit Spreads with Cubic Splines
Maximum Smoothness Forward Credit Spreads
Comparing Results
Data Problems with Risky Issuers
The Case of LIBOR
Determinants of Credit Spread Levels
The Credit Risk Premium: The Supply and Demand for Credit

Conclusion

CHAPTER 18
Legacy Approaches to Credit Risk
The Rise and Fall of Legacy Ratings
Ratings: What They Do and Don’t Do
Through the Cycle vs. Point in Time, a Distinction
without a Difference
Stress Testing, Legacy Ratings, and Transition Matrices
Transition Matrices: Analyzing the Random Changes in
Ratings from One Level to Another

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xvi

Moral Hazard in “Self-Assessment” of Ratings Accuracy
by Legacy Rating Agencies
Comparing the Accuracy of Ratings and Reduced Form Default
Probabilities
Problems with Legacy Ratings in the 2006 to 2011 Credit Crisis
The Jarrow-Merton Put Option and Legacy Ratings

The Merton Model of Risky Debt
The Intuition of the Merton Model
The Basic Merton Model
Valuing Multipayment Bonds with the Merton Model of Risky Debt
Estimating the Probability of Default in the Merton Model
Implying the Value of Company Assets and Their Return Volatility σ
Mapping the Theoretical Merton Default Probabilities to
Actual Defaults
The Merton Model When Interest Rates Are Random
The Merton Model with Early Default
Loss Given Default in the Merton Model
Copulas and Correlation between the Events of Default of
Two Companies
Back to the Merton Case
Problems with the Merton Model: Summing Up
Appendix
Assumptions
Using Ito’s Lemma to Expand Changes in the Value of
Company Equity

CHAPTER 19
Valuing Credit Risky Bonds
The Present Value Formula
Valuing Bonds with No Credit Risk
Simulating the Future Values of Bonds with No Credit Risk
Current and Future Values of Fixed Income Instruments:
HJM Background and a Straight Bond Example
Valuation of a Straight Bond with a Bullet
Principal Payment at Maturity
Valuing an Amortizing Loan

Valuing Risk-Free, Floating-Rate Loans
Valuing Bonds with Credit Risk
Simulating the Future Values of Bonds with Credit Risk
Valuing the Jarrow-Merton Put Option

CHAPTER 20
Credit Derivatives and Collateralized Debt Obligations
Credit Default Swaps: Theory
Credit Default Swaps: Practice
Collateralized Debt Obligations: Theory
Collateralized Debt Obligations: A Worked Example of
Reduced Form Simulation

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Collateralized Debt Obligations: Practice
The Copula Method of CDO Valuation: A Postmortem
Valuing the JarrowÀMerton Put Option

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PART FOUR

Risk Management Applications: Instrument by Instrument
CHAPTER 21
European Options on Bonds
Example: European Call Option on Coupon-Bearing Bond
Example: Coupon-Bearing Bond with Embedded
European Call Option
European Options on Defaultable Bonds
HJM Special Case: European Options in the One-Factor
Vasicek Model
Options on Coupon-Bearing Bonds
The Jarrow-Merton Put Option

CHAPTER 22
Forward and Futures Contracts
Forward Contracts on Zero-Coupon Bonds
Forward Rate Agreements
Eurodollar Futures-Type Forward Contracts
Futures on Zero-Coupon Bonds: The Sydney
Futures Exchange Bank Bill Contract
Futures on Coupon-Bearing Bonds: Dealing with the
Cheapest to Deliver Option
Eurodollar and Euroyen Futures Contracts
Defaultable Forward and Futures Contracts

CHAPTER 23
European Options on Forward and Futures Contracts
Valuing Options on Forwards and Futures:
Notations and Useful Formulas
European Options on Forward Contracts on Zero-Coupon Bonds
European Options on Forward Rate Agreements
European Options on a Eurodollar Futures-Type Forward Contract
European Options on Futures on Coupon-Bearing Bonds
European Options on Money Market Futures Contracts
Defaultable Options on Forward and Futures Contracts

CHAPTER 24
Caps and Floors
Caps as European Options on Forward Rate Agreements
Forming Other Cap-Related Securities
Valuing a Cap
Valuing a Floor
Valuing a Floating Rate Loan with a Cap

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Value of a Loan with a Cap and a Floor
Variations on Caps and Floors
Measuring the Credit Risk of Counterparties on Caps and Floors

CHAPTER 25
Interest Rate Swaps and Swaptions
Interest Rate Swap Basics
Valuing the Interest Rate Swaps
The Observable Fixed Rate in the Swap Market
An Introduction to Swaptions
Valuation of European Swaptions
Valuation of American Swaptions
Defaultable Interest Rate Swaps and Swaptions

CHAPTER 26
Exotic Swap and Options Structures
Arrears Swaps
Digital Option
Digital Range Notes
Range Floater
Other Derivative Securities
Credit Risk and Exotic Derivatives Structures

CHAPTER 27
American Fixed Income Options
An Overview of Numerical Techniques for Fixed
Income Option Valuation
An Example of Valuation of a Callable Bond with a
Three-Factor HJM Bushy Tree
What Is the Par Coupon on a Callable Bond?
An Example of Valuation of a Rationally Prepaid
Amortizing Loan
Monte Carlo Simulation
Conclusions

Finite Difference Methods
Binomial Lattices
Trinomial Lattices
HJM Valuation of American Fixed Income Options
When Default Risk Is Present

CHAPTER 28
Irrational Exercise of Fixed Income Options
Analysis of Irrationality: Criteria for a Powerful Explanation
The Transactions Cost Approach
Irrational Exercise of European Options
The Irrational Exercise of American Options

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A Worked Example Using an Amortizing Loan with
Rational and Irrational Prepayment Behavior
Implied Irrationality and Hedging
Credit Risk and Irrational Prepayment Behavior

CHAPTER 29
Mortgage-Backed Securities and Asset-Backed Securities
Transactions Costs, Prepayments, Default, and Multinomial Logit
Legacy Prepayment Analysis of Mortgage-Backed Securities
Legacy Approaches: Prepayment Speeds and the
Valuation of Mortgages
Constant Prepayment Speeds Are Simply a Principal
Amortization Assumption
Legacy Approaches: Option-Adjusted Spread
Implications for OAV Spread, CMOs, and ARMs
Logistic Regression, Credit Risk, and Prepayment
Mortgage-Servicing Rights: The Ultimate Structured Product
An Introduction to the Valuation of Mortgage-Servicing Rights
Comparing Best Practice and Common Practice in
Valuing and Hedging Mortgage-Servicing Rights
Valuation Yield Curve for Cash Flows
Simulation of Random Movements in Yields
The Role of Home Prices in Defaults and Prepayments
Other Sources of Cash Flow Related to
Mortgage-Servicing Rights
Incorrect Hedging of Mortgage-Servicing Rights
Conclusion

CHAPTER 30
Nonmaturity Deposits
The Value of the Deposit Franchise
Total Cash Flow of Nonmaturity Deposits
Specifying the Rate and Balance Movement Formulas
The Impact of Bank Credit Risk on Deposit Rates and Balances
Case Study: German Three-Month Notice Savings Deposits

The Regulators’ View
Conclusion

CHAPTER 31
Foreign Exchange Markets
Setting the Stage: Assumptions for the Domestic and
Foreign Economies
Foreign Exchange Forwards
Numerical Methods for Valuation of Foreign Currency Derivatives
Legacy Approaches to Foreign Exchange Options Valuation
Implications of a Term Structure Model-Based FX Options Formula
The Impact of Credit Risk on Foreign Exchange Risk Formulas

xix

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650

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675
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680
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CONTENTS

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CHAPTER 32
Impact of Collateral on Valuation Models: The Example of

Home Prices in the Credit Crisis
The Impact of Changing Home Prices on Collateral Values
in the Credit Crisis
Modeling Variations in Collateral Values
The Impact of Collateral Values on a Rationally Prepaid Mortgage
Conclusions about the Impact of Collateral Values

CHAPTER 33
Pricing and Valuing Revolving Credit and Other Facilities
Analyzing Revolving Credit and Other Facilities
Fluctuating Credit Risk and Revolving Credit Drawdowns
Incorporating Links between Credit Quality and Line Usage
Is a Line of Credit a Put Option on the Debt of the Issuer?

CHAPTER 34
Modeling Common Stock and Convertible Bonds on a Default-Adjusted Basis
Modeling Equities: The Traditional Fund Management Approach
Modeling Equities: The Derivatives Approach
Modeling Equities: A Credit RiskÀAdjusted Approach
Options on the Common Stock of a Company That Can Go Bankrupt
Convertible Bonds of a Company That Can Go Bankrupt

CHAPTER 35
Valuing Insurance Policies and Pension Obligations
Life Insurance: Mortality Rates vs. Default Probabilities
Cyclicality in Default Probabilities and Mortality Rates
Valuing Life Insurance Policies
Pension Obligations
Property and Casualty Insurance
The Jarrow-Merton Put Option

682
682
683
684
693

694
695
696
697
697

700
701
702
703
704
706

708
708
711
711
712
713
714

PART FIVE

Portfolio Strategy and Risk Management
CHAPTER 36
Value-at-Risk and Risk Management Objectives Revisited at the
Portfolio and Company Level
The Jarrow-Merton Put Option as a Measure of Total Risk:
An Example
A Four-Question PassÀFail Test for Financial Institutions’
CEOs and Boards of Directors
Why Do These Four Questions Matter?
An Alphabet of 26 Extra-Credit Questions
Is Your Value-at-Risk from Value-at-Risk?

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Contents

VaR vs. the Put Option for Capital Allocation
Why Are the VaR and Put Approaches So Different:
Self-Insurance vs. Third-Party Insurance
Calculating the Jarrow-Merton Put Option Value and
Answering the Key 4 1 26 Questions
Valuing and Simulating the Jarrow-Merton Put Option
What’s the Hedge?
Liquidity, Performance, Capital Allocation, and

Own Default Risk

CHAPTER 37
Liquidity Analysis and Management: Examples from the Credit Crisis
Liquidity Risk Case Studies from the Credit Crisis
Case Studies in Liquidity Risk
Largest Funding Shortfalls
American International Group (AIG)
Consolidated JPMorgan Chase, Bear Stearns, and
Washington Mutual
State Street
Morgan Stanley
Dexia Credit Local New York Branch
Implications of the Credit Crisis History for Liquidity
Risk Management and Analysis
Types of Liquidity Events
Liquidity Risk and Credit Risk Linkages
Measuring Liquidity Risk as a Line of Credit in the
Jarrow-Merton Put Option Sense
Integrating Managerial Behavior and Market Funds Supply
in Liquidity Risk Measurement
Determining the Optimal Liquidity Strategy
Summing Up

CHAPTER 38
Performance Measurement: Plus Alpha vs. Transfer Pricing
Transaction-Level Performance Measurement vs. PortfolioLevel Performance Measurement
Plus Alpha Benchmark Performance vs. Transfer Pricing
Why Default Risk Is Critical in Performance Measurement
of Equity Portfolios

“Plus Alpha” Performance Measurement in Insurance and Banking
Decomposing the Reasons for Plus or Minus Alpha in a Fixed
Income Portfolio
A Worked Example of Modern Fixed Income Performance Attribution
The Jarrow-Merton Put Option and Capital
Using the Jarrow-Merton Put Option for Capital Allocation
Introduction
Using the Jarrow-Merton Put Option Concept for Capital Allocation

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731
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734

735
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CONTENTS

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Extending the Jarrow-Merton Capital Allocation
to a Multiperiod Framework
Summing Up

CHAPTER 39
Managing Institutional Default Risk and Safety and Soundness
Step 1: Admitting the Possibility of Failure
Managing the Probability of Failure
Are Ratings a Useful Guide?
Are CDS Spreads a Useful Guide?

Using Quantitative Default Probabilities
Controlling the Probability of Failure through the Credit Cycle
Hedging Total Risk to Maximize Shareholder Value
Implications for Basel II, Basel III, and Solvency II
Simulating Your Own Probability of Default

CHAPTER 40
Information Technology Considerations
Common Practice in Risk Management Systems: Dealing with
Legacy Systems
Upgrading the Risk Infrastructure: The Request for Proposal Process
Paid Pilots as Final Proof of Concept
Keys to Success in Software Installation
Vendor Size: Larger Vendor or Small Vendor?
Being a Best Practice User

CHAPTER 41
Shareholder Value Creation and Destruction
Do No Harm
Measure the Need to Change
Rating Your Primary Risk System
Master the Politics and Exposition of Risk Management:
Shareholder Value Creation
Daily Management Reporting of Total Risk
Moving from Common Practice to Best Practice
The Senior Management Perspective
The Middle Management Perspective
The Working-Level Perspective
Getting Help to Create Shareholder Value
Postscript

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806

807
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Bibliography

809

Index

819


Introduction: Wall Street
Lessons from Bubbles

T

he credit crisis that began to unfold in the United States and Europe in 2006
contains a treasure trove of lessons for risk managers that we have tried to
incorporate into this book. Since we have each worked in Japan, we felt strongly that
the collapse of the Japanese bubble, which peaked in late 1989, contained equally
useful lessons for risk managers. As you’ll note in the “key fallacies in risk management” discussed below, many ignored the lessons of the Japanese bubble because
of the common fallacy that “if it hasn’t happened to me yet, it won’t happen to me,
even if it’s happened to someone else.”
Now that the United States and much of Europe are experiencing the collapse of
a bubble much like that which burst in Japan, the lessons from each of these bubbles
seem much more relevant to risk managers around the world.

We have worked hard in the second edition of this book to severely deemphasize the discussion of financial models that are obviously inaccurate, misleading, or clearly inferior to another modeling approach. We make this judgment on
the basis of cold hard facts (via model testing) or because of assumptions that are
known to be false. The list of models that failed under the duress of the credit crisis is
a long one, and we make no apologies for reflecting those failures in this book.
We’ve also worked hard to explain which models performed well during the credit
crisis. Again, we base that judgment on model testing and the logical consistency and
accuracy of the assumptions behind those models.
We believe in a “multiple models approach” to risk management. That doesn’t
mean, however, that all models used are equally accurate. Nothing could be further
from the truth. The use of a multiple models approach, however, makes it clear when
a better model has been brought to the risk management discipline and when it’s time
for an older model to be removed from the toolkit. One of our British friends provided the elegant observation that “I don’t think it’s gentlemanly to compare the
accuracy of two models.” The authors, by contrast, believe that such comparisons
are a mandatory part of corporate governance and best practice risk management.
With that brief introduction, we turn to a short summary of common fallacies in
risk management that have been exposed as fallacies very starkly in the wake of the
recent credit crisis.

KEY FALLACIES IN RISK MANAGEMENT
Summarizing the dangerous elements of conventional wisdom in risk management isn’t
easy. We’ve restricted ourselves to the seven most dangerous ways of thinking about risk.
Each of them has much in common with this famous quote of John Maynard Keynes from

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