Abstract
In recent years the quantification of credit risk has become an important topic in research and in finance and banking. This has been accelerated by the reorganisation of the Capital Adequacy Framework (Basel II).
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Notes
- 1.
Basel Committee on Banking Supervision (2004).
- 2.
- 3.
Schuermann (2004).
- 4.
- 5.
Gupton et al. (2000).
- 6.
- 7.
- 8.
Recovery rates greater than one are unusual. In these cases the bond is traded above par after the issuer defaults. These values are excluded from the dataset in the empirical research, see Sect. 8.3.1.
- 9.
This transformation ensures a range between 0 and 1 of the estimated and predicted LGD.
- 10.
Wolfinger et al. (1994).
- 11.
This constraint naturally only affects borrowers who defaulted several times. Furthermore, observations with LGD equal to zero and negative LGD are excluded from the analysis, because the transformed LGD y t(i) cannot be calculated. If the recovery rate is greater than 1, i.e. if the market value of a bond one month after default is greater than the nominal value of the bond, the LGD becomes negative. In the dataset this was the case in 0.5% of all observations.
- 12.
The (aggregated) sector “industry” contains the sectors “industrial”, “transportation” and “other non-bank” of Moody’s sectoral classification (with 12 sectors) in Moody’s Default Risk Service (DRS) database. For reason of completeness one has to know that there are two other aggregated sectors. On the one hand there is the (aggregated) sector “financial service providers” containing the sectors “banking”, “finance”, “insurance”, “real estate finance”, “securities”, “structured finance” and “thrifts” and on the other hand the (aggregated) sector “sovereign/public utility” containing the sectors “public utility” und “sovereign”. This aggregation was made as several sectors did not have enough observations.
- 13.
In principle, only issuers with one bond could be left in the dataset if the effect of several bonds per issuer should be eliminated. As this restriction would lead to relatively few observations, only issuers with five or more bonds are excluded. Hence the dataset is only diminished by 4%.
- 14.
For withdrawn ratings, Moody’s uses a class “WR”. Because of the lagged consideration of rating there are no bonds in the dataset with rating “WR” one year before default.
- 15.
Moody’s used to name this rating class with “Caa” until 1997. Since 1998, this class has been separated into the three rating classes “Caa1”, “Caa2” and “Caa3”. To use the data after 1998, the latter three ratings have been aggregated in one rating class which is named “Caa” in the following.
- 16.
For a consideration of the hierarchy of seniority classes see Schuermann (2004, p. 10).
- 17.
A list of potential macroeconomic factors can be found in the appendix.
- 18.
Additionally, models for all sectors are estimated containing dummy variables for the different sectors in addition to the variables mentioned below. The use of a single sector leads to more homogenous data.
- 19.
In general, all interpretations according to the quoted model refer to the transformed LGD y t(i). As y t(i) is the result of a strictly monotonic transformation of LGD all interpretations hold as well for LGD.
- 20.
Hamilton and Carty (1999).
- 21.
Altman et al. (2003) also detected a relationship between the average LGD per year and the volume of defaulted bonds.
- 22.
For example the issuer rating could be “Aaa” and the debt rating “A”.
- 23.
\( {\sigma^2} = b_1^2 + b_2^2 \).
- 24.
\( \omega = b_1^2/{\sigma^2} \).
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Appendix: Macroeconomic Variables
Appendix: Macroeconomic Variables
Interest Rate Fed Fund – monthly |
Interest Rate Treasuries, constant maturity 6 months, nominal, monthly |
Interest Rate Treasuries, constant maturity 1 year, nominal, monthly |
Interest Rate Treasuries, constant maturity 5 years, nominal, monthly |
Interest Rate Treasuries, constant maturity 7 years, nominal, monthly |
Interest Rate Treasuries, constant maturity 10 years, nominal, monthly |
Interest Rate Conventional mortgages, fixed rate – monthly |
Commercial bank interest rates, 48-month new car, quarterly |
Commercial bank interest rates, 24 months personal, quarterly |
Commercial bank interest rates, all credit card accounts, quarterly |
Commercial bank interest rates, Credit card accounts, assessed interest |
Interest Rate, new car loans at auto finance companies, monthly |
Interest Rate, bank prime loan, monthly |
Civilian Labour Force Level |
Employment Level |
Unemployment Level |
Unemployment rate |
Initial Claims for Unemployment Insurance |
Challenger Report, Announced Layoffs |
Mass Layoffs |
Manufacturing Data: |
Shipments Total Manufacturing |
New Orders Total Manufacturing |
Unfilled Orders Total Manufacturing |
Inventory Total Manufacturing |
Inventory to shipments Total Manufacturing |
Capacity Utilization total |
Business Bankruptcy Filings |
Non-business Bankruptcy Filings |
Total Bankruptcy Filings |
Dow Jones Industrial Index |
S&P500 |
NASDAQ100 |
Price Indices: |
GDP Implicit Price Deflator (2000 = 100) |
Consumer Price Index, All Urban Consumers; U.S. city average, all items |
Producer Price Index; U.S. city average, Finished Goods |
Gross Domestic Product |
Gross Private Domestic Investment |
Percent Change From Preceding Period in Real Gross Domestic Product |
Public Debt |
Tax Revenues |
Uni Michigan Consumer Sentiment Index |
PMI (Purchase Manager Index, Institute for Supply Management) |
Retail Sales total (excl. Food Services) |
Revised Estimated Monthly Sales of Merchant Wholesalers |
Business Cycle Indicator: Index of Leading Indicators (The Conference Board) |
Average crude oil import costs (US$/barrel) |
Average default rate of issuers at the bond market |
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Hamerle, A., Knapp, M., Wildenauer, N. (2011). Modelling Loss Given Default: A “Point in Time”-Approach. In: Engelmann, B., Rauhmeier, R. (eds) The Basel II Risk Parameters. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16114-8_8
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