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Affiliations: IMF (Alter); Federal Reserve Bank of Cleveland (Craig); Deutsche Bundesbank (Raupach). We are very thankful for comments from Günter Franke, Andrew Haldane, Moritz Heimes, Christoph Memmel, Camelia Minoiu, Rafael Repullo, Almuth Scholl, Vasja Sivec, Martin Summer, Alireza Tahbaz-Salehi, participants at the Annual IJCB Research Conference hosted by the Federal Reserve Bank of Philadelphia, the Final Conference of the Macro-prudential Research Network (MaRs) hosted by the ECB, the EUI Conference on Macroeconomic Stability, Banking Supervision and Financial Regulation, and seminar participants at the Bundesbank and the IMF. This working paper is forthcoming in International Journal of Central Banking. This working paper represents the authors’ personal opinions and do not necessarily reflect the views of the Deutsche Bundesbank or its staff, the Eurosystem, the Federal Reserve Bank of Cleveland, the International Monetary Fund (IMF), its Executive Board, or IMF policies. All remaining errors are our own.
By incorporating credit migrations and correlated exposures, we differ from most of the literature on interbank contagion that usually studies idiosyncratic bank defaults; see Upper (2011). Elsinger et al. (2006) and Gauthier et al. (2012) are remarkable exceptions.
As already mentioned, Elsinger et al. (2006) and Gauthier et al. (2012) do model correlated portfolio losses, however for the Austrian and the Canadian banking system, which both consist of much fewer banks than the German system.
This assumption could be relaxed but would require the inclusion of other data sources. In the simulations we use a value of 0.20, which is very close to a value reported by Zeng and Zhang (2001). It is the average over their sub-sample of firms with the lowest number of missing observations.
We use the 1981–2010 average one-year transition matrix for a global set of corporates (Standard and Poor’s, 2011).
The borrower statistics report exposures in three maturity buckets. Exposure-weighted averages of maturities indicate only small maturity differences between BS sectors. By setting the maturity to 4 years we simplify loan pricing substantially, mainly since the calculation of sub-annual migration probabilities is avoided.
We have chosen values reported by Davydenko and Franks (2008), who investigate LGDs of loans to German corporates, similar to Grunert and Weber (2009), who find a very similar standard deviation of 0.36 and a somewhat lower mean of 0.275.
Market spreads are derived from a daily time series of Merill Lynch euro corporate spreads covering all maturities, from April 1999 to June 2011. The codes are ER10, ER20, ER30, ER40, HE10, HE20, and HE30. Spreads should rise monotonically for deteriorating credit. We observe that the premium does rise in general but has some humps and troughs between BB and CCC. We smooth these irregularities out as they might have substantial impact on bank profitability but lack economic reason. To do so, we fit Ereturn (R0) by a parabola, which turns out to be monotonous, and calibrate spreads afterwards to make the expected returns fit the parabola perfectly. Spread adjustments have a magnitude of 7bp for A– and better, and 57bp for BBB+ and worse. Ultimate credit spreads for ratings without notches are: AAA: 0.47%; AA: 0.66%; A: 1.22%; BBB 2.2476%; BB: 4.10%; B: 8.35%; CCC–C: 16.40%.
This idea is the basis of asymptotic credit risk models. The model behind Basel II is an example of this model class.
The density of a network is the ratio of the number of existing connections divided by the total number of possible links. In our case of a directed network, the total number of possible links is 1764 χ 1763 = 3,109, 932.
In our analysis we set φ = 0.5, leading to the geometric mean between strength and degree.
The Bundesbank labels this database as Gross- und Millionenkreditstatistik. A detailed description of the database is given by Schmieder (2006).
Loan exposures also have to be reported if they are larger than 10% of a bank’s total regulatory capital. If such an exposure falls short of €1.5 mn, it is not contained in our dataset of large exposures. Such loans represent a very small amount compared to the exposures that have to be reported when exceeding €1.5 mn; they are captured in the Borrower Statistics though and hence part of the “small loans”; see Section B..
It is also important to notice that, while the data are quarterly, the loan volume trigger is not strictly related to an effective date. Rather, a loan enters the database once its actual volume has met the criterion at some time throughout the quarter. Furthermore, the definition of credit triggering the obligation to report large loans is broad: besides on-balance sheet loans, the database conveys bond holdings as well as off-balance sheet debt that may arise from open trading positions, for instance. We use total exposure of one entity to another. Master data of borrowers contains its nationality as well as assignments to borrower units, when applicable, which is a proxy for the joint liability of borrowers. We have no information regarding collateral in this dataset.
Each lender is considered at an aggregated level (i.e. as “Konzern”). At single-entity level there are more than 4.000 different lending entities who report data.
We consider exposures to the public sector to be risk-free (and hence exclude them from our risk engine) since the federal government ultimately guarantees for all public bodies in Germany.
The main sectors are agriculture, basic resources and utilities, manufacturing, construction, wholesale and retail trade, transportation, financial intermediation and insurance, and services.
A financial institution has to submit BS forms if it is a monetary financial institution (MFI), which does not necessarily coincide with being obliged to report to the LED. There is one state-owned bank with substantial lending that is exempt from reporting BS data by German law. As it is backed by a government guarantee, we consider this bank neutral to interbank contagion.
Tables with these measures are available on request.
Source: Deutsche Bundesbank’s Monthly Report, March 2011.
One aspect that needs to be mentioned here is that the observed IB network is not the complete picture, since interbank liabilities of German banks raised outside Germany are not reported to the LED. For example, the LED captures a loan made by Goldman Sachs to Deutsche Bank only if it is made by Goldman Sachs’ German subsidiary. This aspect might bias downwards centrality measures of big German banks that might borrow outside Germany.
Foreign bank exposures are included in Sector 17 of the “real economy” portfolio, since we have to exclude them from the interbank network. Loans made by foreign banks to German financial entities are not reported to the LED, except they are made by a subsidiary registered in Germany. These subsidiaries are part of our interbank network.
We do not have any information related to collateral or the seniority of claims.
We could also search for a solution for
Our results remain robust also for other values ϕ ∊ (1%, 3%, 10%}. Alessandri, Gai, Kapadia, Mora, and Puhr (2009) and Webber and Willison (2011) use contagious BCs as a function of total assets, and set ϕ to 10%. Given the second term of our BC function that incorporates fire sales effects, we reach at a stochastic function with values between 5% and 15% of total assets.
We acknowledge that real-world BCs would probably be sensitive to the amount of interbank credit losses, which we ignore. This simplification, however, allows us to calculate potential BCs before we know which bank will default through contagion, such that we do not have to update BCs in the contagion algorithm. If we did, it would be difficult to preserve proportional loss sharing in the Eisenberg-Noe allocation.
To check the numerical stability of our results, we re-ran several times the computation of VaR measures at quantile α = 99.9%. For this computation we employed a new set of one million simulations, and kept the same PDs for loans where unreported values had been reported by random choices. Results are very similar with an average variance of under 2%. VaR measures at 99% have a variance of under 0.5%.
Default probabilities for these loans are taken from the Large Exposure Database in the same way as for loans to the real economy.
If banks held exactly Kmin,i as capital, actual bank PDs after contagion could be below or above 1 percent, depending on whether quantiles of portfolio losses in a risk model where interbank loans are directly driven by systematic factors are larger than in presence of contagion (but without direct impact of systematic factors). However, the probability of bank defaults through fundamental losses cannot exceed 1 percent, given that asset correlations in the factor model are positive.