Abstract
This paper extends the existing literature on deposit insurance by proposing a new approach for the estimation of the loss distribution of a Deposit Insurance Scheme (DIS) that is based on the Basel 2 regulatory framework. In particular, we generate the distribution of banks’ losses following the Basel 2 theoretical approach and focus on the part of this distribution that is not covered by capital (tail risk). We also refine our approach by considering two major sources of systemic risks: the correlation between banks’ assets and interbank lending contagion. The application of our model to 2007 data for a sample of Italian banks shows that the target size of the Italian deposit insurance system covers up to 98.96% of its potential losses. Furthermore, it emerges that the introduction of bank contagion via the interbank lending market could lead to the collapse of the entire Italian banking system. Our analysis points out that the existing Italian deposit insurance system can be assessed as adequate only in normal times and not in bad market conditions with substantial contagion between banks. Overall, we argue that policy makers should explicitly consider the following when estimating DIS loss distributions: first, the regulatory framework within which banks operate such as (Basel 2) capital requirements; and, second, potential sources of systemic risk such as the correlation between banks’ assets and the risk of interbank contagion.
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Notes
Fund adequacy is analysed as far as its size is concerned. The analysis of contributions arrangements and the timing of money availability are beyond the scope of this paper.
A further extension of the traditional option pricing approach is provided by Episcopos (2004), who applies the concept of vulnerable option to deposit insurance. With respect to the more commonly applied option framework, this extension takes into account not only the relevance of the each bank’s risks, but also the risks of the guarantor. However, in contrast to the analyses described above, this approach does not require the derivation of any loss distribution in order to set DIS funds.
See Appendix for details.
The credit quality of the asset portfolio influences also the value of the expected losses (EL _{ j }): banks with more risky assets will show higher values of EL _{ j }.
This can be clearly understood by dividing both members in Eq. 1 by total assets. Under this new specification, a lower risk of default is associated to a higher bank capital ratio (the ratio between equity capital and total assets).
We thank an anonymous referee for raising the issue of the relevance of considering firm heterogeneity when we model credit risk. On this aspect see Hanson et al. (2008).
When a bank fails, we consider that the creditors in the interbank market are facing a liquidity risk. This liquidity risk is equal to the total amount of interbank credits that the other banks have lent to the defaulted bank.
As our approach models only credit risk, it is worthwhile to analyse how relevant this risk is in our sample. To this end, we examine the distribution of the weights of the credit risk capital requirements over the total capital requirements for each bank. We observe a mean value of over 91% (st. dev. of 18%). The credit risk therefore is the most important source of regulatory risk in our sample.
Since the capital requirements disclosed by the Italian banks in 2007 still refer to the rules established by Basel I, our estimates assume that the regulatory shift due to the adoption of an FIRB approach does not modify these requirements. Although we acknowledge the simplifications behind this assumption, it is worth emphasising that one of the purposes that the new regulatory framework is to avoid substantial changes in the capital requirements applied to banks (Cannata and Quagliariello 2009).
We thank an anonymous referee for suggesting this testing approach.
Banks are split in three sizebased buckets (total assets): up to 1,000 m€; larger than 1,000 and up to 10,000 m€; over 10,000 m€. Buckets are chosen in order to achieve a balance between the number of banks in each bucket and the share of total assets it represents.
Also in this second test we assume the mean of the correlation distribution to be equal to that of the basic scenario.
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Acknowledgments
We are grateful to Ed Altman, J. Dermine and an anonymous reviewer for helpful comments on an earlier draft of this paper.
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The opinions presented here are exclusively those of the authors and do not in any way represent those of the European Commission.
Appendix
Appendix
The computation of capital requirements in the Basel 2 Internal RatingsBased (IRB) approach
In the IRB approach, the capital requirement (CR) for a single exposure is computed according to the following formula:
Where:

PD is the obligor probability of default;

LGD is the loss given default;

M is the time to maturity;

B is a function of PD computed as \( B = {\left[ {0.11852  0.05478\ln \left( {PD} \right)} \right]^2} \))

R is the correlation factor computed as follows:
$$ R = 0.12\frac{{\left[ {1  EXP\left( {  50 \times PD} \right)} \right]}}{{\left[ {1  EXP\left( {  50} \right)} \right]}} + 0.24 \times \left[ {1  \frac{{\left( {1  EXP\left( {  50 \times PD} \right)} \right)}}{{\left( {1  EXP\left( {  50} \right)} \right)}}} \right]  0.04 \times \left[ {1  \frac{{\left( {S  5} \right)}}{{45}}} \right] $$(2)where S is the size of the firm.
Given the assumption of infinite granularity, the overall capital requirement for a bank j is computed as the sum of the capital requirements of each loan exposure l:
that is the sum of the capital allocation parameter (CR) of each exposure l multiplied by its amount Al.
We can derive the average PD of a bank’s asset portfolio needed to compute the asset losses as
where Kj is the total value of the capital requirements for the bank j.
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De Lisa, R., Zedda, S., Vallascas, F. et al. Modelling Deposit Insurance Scheme Losses in a Basel 2 Framework. J Financ Serv Res 40, 123–141 (2011). https://doi.org/10.1007/s1069301000970
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DOI: https://doi.org/10.1007/s1069301000970
Keywords
 Deposit insurance
 Basel 2
 Systemic risk
 Contagion risk
 Financial safety net
JEL Classification
 G21
 G22