1. Credit Value at Risk Chapter 18
Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012

2. Rating Transitions
One year rating transition probabilities are published by rating agencies.
If we assume that the rating transition in one period is independent of that in other periods we can calculate the rating transition for any period (see Appendix J and software)
The “ratings momentum” phenomenon means that the independence assumption is not perfectly correct
Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012

3. One-Year Rating Transition Matrix (% probability, Moody’s 1970-2010) Table 18.1 page 401
Initial
Rating
Aaa Aa A
Baa Ba B
Caa
Ca-C
Default
90.42
8.92
0.62
0.01
0.03
0.00
1.02
90.12
8.38
0.38
0.05
0.02
0.06
2.82
90.88
5.52
0.51
0.11
0.19
4.79
89.41
4.35
0.82
0.18
0.41
6.22
83.43
7.97
0.59
0.09
1.22
0.04
0.14
5.32
82.19
6.45
0.74
4.73
0.16
0.53
9.41
68.43
4.67
16.76
0.39
2.85
10.66
43.54
42.56
100.00
Rating at year end
Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012

4. Five-Year Rating Transition Matrix (calculated from one-year transitions) Table 18.2 page 401
Initial
Rating
Aaa Aa A
Baa Ba B
Caa
Ca-C
Default
61.12
29.99
7.70
0.89
0.21
0.05
0.01
0.00
0.03
3.45
61.89
28.70
4.71
0.73
0.25
0.07
0.19
0.44
9.72
65.78
18.88
3.24
1.06
0.24
0.04
0.60
0.22
1.69
16.38
60.98
12.93
4.64
0.97
0.13
2.06
3.40
18.20
44.69
20.07
3.70
0.52
8.92
0.20
0.83
3.27
13.28
43.05
11.49
1.64
26.21
0.08
0.23
0.93
3.52
16.80
18.67
2.93
56.84
0.02
0.06
0.31
1.39
5.89
6.78
2.40
83.15
100.00
Rating at end
Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012

5. One-Month Rating Transition Matrix (calculated from one-year transitions) Table 18.3 page 401
Initial
Rating
Aaa Aa A
Baa Ba B
Caa
Ca-C
Default
99.16
0.82
0.02
0.00
0.09
99.12
0.77
0.01
0.26
99.18
0.51
0.04
0.44
99.05
0.41
0.06
0.59
98.46
0.79
0.03
0.53
98.32
0.70
0.07
0.36
1.01
96.79
0.67
1.48
0.28
1.53
93.23
4.92
100.00
Rating at month end
Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012

6. Credit VaR (page 321) Can be defined analogously to Market Risk VaR
A one year credit VaR with a 99.9% confidence is the loss level that we are 99.9% confident will not be exceeded over one year
Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012

7. Vasicek’s Model (Equation 18.1, page 402)
For a large portfolio of loans, each of which has a probability of Q(T) of defaulting by time T the default rate that will not be exceeded at the X% confidence level is
Where r is the Gaussian copula correlation
Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012

8. VaR Model (Equation 18.2, page 402)
Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012

9. Credit Risk Plus (Section 18.3, page 403)
This calculates a loss probability distribution using a Monte Carlo simulation where the steps are:
Sample overall default rate
Sample probability of default for each counterparty category
Sample number of losses for each counterparty category
Sample size of loss for each default
Calculate total loss from defaults
This is repeated many times to calculate a probability distribution for the total loss
Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012

10. CreditMetrics (Section 18.4, page 405)
Calculates credit VaR by considering possible rating transitions
A Gaussian copula model is used to define the correlation between the ratings transitions of different companies
Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012

11. The Copula Model : xA and xB are sampled from correlated standard normals
Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012

12. Credit Risk in the Trading Book: The Specific Risk Charge
To calculate the specific risk charge, banks must model credit spreads to calculate a 10-day 99% VaR
Alternatives:
Historical simulation
10-day transition matrix
Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012

13. Credit Risk in the Trading Book: Incremental Risk Charge
Banks must calculate a one year 99.9% VaR
This is to ensure that capital is similar to the capital that would be charged if the instrument were in the banking book
They are allowed to make a constant level of risk assumption (minimum liquidity horizon is three months)
Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012

14. Constant Level of Risk Assumption
Suppose a bank has a BBB bond and uses a liquidity horizon of 3 months
At the end of each month period the bond, if it has deteriorated is assumed to be sold and replaced with a new BBB bond
The one-year loss is then replaced by four three-month losses
Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012