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Modelling Deposit Insurance Scheme Losses in a Basel 2 Framework

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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

  1. 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.

  2. 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.

  3. See Appendix for details.

  4. 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 .

  5. 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).

  6. 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).

  7. 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.

  8. 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.

  9. 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).

  10. We thank an anonymous referee for suggesting this testing approach.

  11. Banks are split in three size-based 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.

  12. Also in this second test we assume the mean of the correlation distribution to be equal to that of the basic scenario.

References

  • Baele L, De Jonghe O, Vander VR (2007) Does the stock market value bank diversification? J Bank Finance 31:1999–2023

    Article  Google Scholar 

  • Basel Committee on Banking Supervision (2004, June) International Convergence of Capital Measurement and Capital Standards. A Revised Framework

  • Basel Committee on Banking Supervision (2005, July) An Explanatory Note on the Basel II IRB Risk Weight Functions

  • Cannata F, Quagliariello M (2009) The role of Basel II in the subprime financial crisis: guilty or not guilty. Carefin Working Paper, 03/09

  • DeBandt O, Hartmann P (2000) Systemic risk: a survey. Working paper 35, European Central Bank, Frankfurt, Germany

  • De Jonghe O (2010) Back to the basics in banking? A micro-analysis of banking system stability. J Financ Intermed 19:387–417

    Article  Google Scholar 

  • Dev A, Li S, Wan Z (2006) An analytical model for the FDIC deposit insurance premium. Working paper series, (available at SSRN)

  • Duffie D, Jarrow R, Purnanandam A, Yang W (2003) Market pricing of deposit insurance. J Financ Serv Res 24:93–119

    Article  Google Scholar 

  • Elsinger H, Lehar A, Summer M (2006) Risk assessment for banking systems. Manage Sci 52:1301–1314

    Article  Google Scholar 

  • Episcopos A (2004) The implied reserves of the Bank Insurance Fund. J Bank Finance 28:1617–1635

    Article  Google Scholar 

  • Furfine CH (2003) Interbank exposure: quantifying the risk of contagion. J Money Credit Bank 35:111–128

    Article  Google Scholar 

  • Gordy MB (2003) A risk factor model foundation for ratings-based capital rules. J Financ Intermed 12:199–232

    Article  Google Scholar 

  • Hanson SG, Pesaran MH, Schuermann T (2008) Firm heterogeneity and credit risk diversification. J Empir Finance 15:583–612

    Article  Google Scholar 

  • Huang X, Zhou H, Zhu H (2010) Assessing the systemic risk of a heterogeneous portofolio of banks during the recent financial crisis. BIS Working paper n. 296

  • Jarrow RA, Madam DB, Unal H (2006) Designing countercyclical and risk based aggregate deposit insurance premia. FDIC, Center For Financial Research Working Paper No. WP 2007-02

  • Jokipii T, Milne A (2008) The cyclical behaviour of European Bank capital buffers. J Bank Finance 32:1440–1451

    Article  Google Scholar 

  • Jokipii T, Milne A (2010) Bank capital buffer and risk adjustment decisions. J Financ Stab, Forthcoming

  • Kuritzkes A, Schuermann T, Weiner SM (2005) Deposit insurance and risk management of the U.S. banking system: what is the loss distribution faced by the FDIC. J Financ Serv Res 27:217–242

    Article  Google Scholar 

  • Markus A, Shaked I (1984) The valuation of FDIC deposit insurance using option-pricing estimates. J Money Credit Bank 16:446–460

    Article  Google Scholar 

  • Merton RC (1974) On the pricing of corporate debt: the risk structure of interest rates. J Finance 29:449–470

    Article  Google Scholar 

  • Repullo R, Suarez J (2004) Loan pricing under Basel capital requirements. J Financ Intermed 13:496–521

    Article  Google Scholar 

  • Ronn E, Verma A (1986) Pricing risk adjusted deposit insurance: an option-based approach. J Finance 41:871–895

    Article  Google Scholar 

  • Santos JAC (2000) Bank capital regulation in contemporary banking theory: a review of the literature. BIS Working paper, 90, September

  • Schuermann T, Stiroh KJ (2006) Visible and hidden risk factors for banks. FRB of New York Staff Report, May 2006, n. 252

  • Sironi A, Maccario A, Zazzara C (2004) Credit risk models: an application to deposit insurance pricing. SDA BOCCONI Research Division Working Paper No. 03-84

  • Stolz S, Wedow M (2009) Banks’ regulatory capital buffer and the business cycle: evidence from Germany. J Financ Stab, Forthcoming

  • Vasicek O (1987) Probability of loss on loan portfolio, KMV Corporation (available at www.kmv.com)

  • Vasicek O (1991) Limiting loan loss probability distribution, KMV Corporation (available at www.kmv.com)

  • Vasicek O (2002) Loan portfolio value, Risk December, 160–162

  • Wagner W (2010) Diversification at financial institutions and systemic crises. J Financ Intermed 19:330–356

    Article  Google Scholar 

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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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Correspondence to Riccardo De Lisa.

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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 Ratings-Based (IRB) approach

In the IRB approach, the capital requirement (CR) for a single exposure is computed according to the following formula:

$$ CR = \left[ {LGD \times N\left[ {\sqrt {{\frac{1}{{1 - R}}}} {N^{{ - 1}}}(PD) + \sqrt {{\frac{R}{{1 - R}}}} {N^{{ - 1}}}(0.999)} \right] - PD \times LGD} \right] \times {(1 - 1.5 \times B)^{{ - 1}}} \times [1 + (M - 2.5) \times B] \times 1.06 $$
(1)

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:

$$ {K_j} = \sum\limits_l {CR\left( {P{D_l}} \right){A_l}} $$
(3)

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

$$ PD_j^{ * }\left| {CR\left( {PD_j^{ * }} \right)\sum\limits_l {{A_l}} } \right. = {K_j} $$
(4)

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/s10693-010-0097-0

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