An Introduction to Credit Risk with a Link to Insurance
R.J.A. Laeven, University of Amsterdam and Mercer Oliver Wyman
R.J. de Barbanson, Zanders & Partners
AFIR Colloquium 2003 Maastricht
September 18, 2003
Actuarieel Genootschap – AFIR Working Party Credit Risk

Outline
• Motivation
• Empirical relation between credit spreads and interest rates
• Credit risk models
• Accounting and regulation
Actuarieel Genootschap – AFIR Working Party Credit Risk

Motivation I
• Increase in credit risk on the Euro financial markets due to:
– Introduction of the Euro
– Stability and Growth Pact
Actuarieel Genootschap – AFIR Working Party Credit Risk

Motivation II
1 0 0 %
8 0 %
6 0 %
4 0 %
2 0 %
0 %
7 %
4 5 %
4 8 %
1 8 %
4 1 %
4 1 %
2 7 %
3 9 %
3 4 %
2 0 0 0
C o rp o ra t e : N o n -f in a n c ia l
C o rp o ra t e : Fin a n c ia l
G o v e rn m e n t
V o lu m e ( b illio n s)
5 0 0
3 4 %
4 0 0
3 3 %
3 0 0
3 3 %
2 0 0 1
2 0 0
1 9 9 8 1 9 9 9
Actuarieel Genootschap – AFIR Working Party Credit Risk

Credit Spreads vs Interest Rates I
• Decomposition of the yield-to-maturity on a credit risky asset:
Yield-to-maturity
Credit spread
Liquidity premium
Non-systematic expected default premium
Systematic risk premium
Swap rate Swap rate
Actuarieel Genootschap – AFIR Working Party Credit Risk

Credit Spreads vs Interest Rates II
• Database of Eurobonds (January 1999 until
December 2001)
AAA
AA
A
BBB
< BBB
Average credit spread (b.p.)
-0,02
19,33
51,33
80,7
512,76
Actuarieel Genootschap – AFIR Working Party Credit Risk

Credit Spreads vs Interest Rates III
• Model specification:
 s t , i
 
0 i
 
1 i
 r t
6 m
• Empirical results:
 
2 i
 d t
6 m , 10 y   t , i
AAA
AA
A

1
-0,0207
-0,0805
-0,1889
BBB -0,1344
< BBB -1,6197
Prob.
0,0001
0,0123
0,0003
0,0279
0,0383

2
0,0068
-0,0614
-0,0990
-0,0782
-0,6271
Prob.
0,4569
0,0143
0,0059
0,1386
0,1921
Actuarieel Genootschap – AFIR Working Party Credit Risk

Consequences for ALM
• Inferior hedging quality of credit risky assets
• Risk assessment of the debt portfolio is indispensable
Actuarieel Genootschap – AFIR Working Party Credit Risk

Measurement of Credit Risk
• Influence of both bond portfolio selecting
(return) and sensitivity (risk) increase
• 3 models:
– CreditMetrics (JP Morgan)
– KMV (Moody’s KMV)
– CreditRisk+ (CSFB)
Actuarieel Genootschap – AFIR Working Party Credit Risk

Definition Credit Risk
• Expected Loss =
1) Default Probability x Amount Outstanding x
1 - Recovery Rate
2) Cost of Doing Business
• Unexpected Loss =
Deviation of Expected Loss
Actuarieel Genootschap – AFIR Working Party Credit Risk

CreditMetrics
• CM estimates value of bond at end of credit-risk horizon ( e.g. 1 year) by combining transition (
“migrate from one rating class to another?”
) and possible forward curves ( AAA, AA, ..) t=0 t=1
BBB
AAA
AA
A
BBB
BB
B
CCC
D
Migration Prob. Possible Forward Value
0.02% 109.37
0.33%
5.95%
86.93%
5.30%
1.17%
0.12%
0.18%
109.19
108.66
107.55
102.02
98.10
83.64
51.13
100.00%
Actuarieel Genootschap – AFIR Working Party Credit Risk
Mean= 107.09

KMV Model
• “Equity is call-option on asset value”
• Default probability is estimated on market information (stock price and volatility interest rate structure), financial statements, and (subjective) risk perceptions
• Default probability is used to calculate (un) expected loss
Actuarieel Genootschap – AFIR Working Party Credit Risk

CreditRisk+
• CR+ assumes two states
1) Default, and 2) Non-default
• Default frequency ~ Poisson
• Recovery rate changes through time

Losses follow a density distribution
Actuarieel Genootschap – AFIR Working Party Credit Risk

Comparison
Similarities
• EL= Default prob. x
Exposure x
(1 -recovery rate)
• EL and UL is output
Differences
• Rating (CM/CR+) vs.
Stock price (KMV)
• Spread risk (CM) vs.
default risk
CR+/KMV)
• Market model (CM) vs.
Default model
(CR+/KMV)
Actuarieel Genootschap – AFIR Working Party Credit Risk

Remarks
• CR+ model for hold-to-maturity portfolio
• CM model for available-for-sale portfolio
• KMV is an arbitrage model, that can be used to compare implied price and market price of credit risk
Actuarieel Genootschap – AFIR Working Party Credit Risk

Credit Risk and Regulation
• EU solvency system is now based on 3 pillars:
1) assets, 2) technical provision, and 3) required solvency margin
• Solvency II in progress:
– 1) Estimation of total risk (among other risk due credit, underwriting, market, etc.
), and
2) Impact on Risk Based Capital
– White paper Solvency Test PVK ( FTK )
Actuarieel Genootschap – AFIR Working Party Credit Risk

Credit Risk and Accounting
• Implementation of IAS/IFRS Rules
– IAS39 distinguishes between the valuation methodology of asset portfolios
– Portfolios qualified as hold-to-maturity should be valued at amortized costs (CreditRisk+ …)
– Portfolios qualified as available-for-sale should be valued at fair value (CreditMetrics …)
Actuarieel Genootschap – AFIR Working Party Credit Risk

Questions?
Actuarieel Genootschap – AFIR Working Party Credit Risk