Risk management of deposit insurance corporations with risk-based premiums and credit default swaps

Abstract

In this paper, we propose a risk-based model for deposit insurance premiums and provide the closed-form formula for premiums, including early closure, capital forbearance, interest rate risk, and moral hazard. Our numerical analysis confirms the proposed pricing formula and the relative impact of the provisions for deposit insurance premiums. We illustrate how to use credit default swaps (CDSs) to manage the bank’s asset risk corresponding to the deposit insurance model. A failed bank, Washington Mutual, is used to demonstrate how to calibrate the model’s parameters and calculate fair premiums that are consistent with market risks on the basis of our proposed model and credit derivatives. Finally, a numerical experiment is designed to determine the optimal hedge ratio, which can minimise the variance of cash-flow of the deposit insurance corporations.

Keywords:

• Deposit insurance
• Moral hazard
• Capital forbearance
• Credit default swaps

JEL Classification:

• C51
• G21
• G32

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Demirguc-Kunt and Detragiache (2002) find that deposit insurance exacerbates moral hazard problems in a bank lending scenario and is associated with a high likelihood of a banking crisis. So and Wei (2004) observe that the effect of moral hazard on fair insurance premiums is more significant than the effect of bank’s equity and charter values. An insurer should be able to deter banks’ risky behavior and close problematic banks when necessary. Therefore, VanHoose (2007) specifies that the fair pricing framework for deposit insurance is crucial to mitigate moral hazard problems. Anginer et al. (2014) investigate the relations between deposit insurance and moral hazard for different periods. Their study finds that deposit insurance increases moral hazard and makes financial systems more vulnerable to crises during normal times.

2 https://www5.fdic.gov/sdi/main.asp?formname=compare

3 In the table, reserves are defined as ‘cash and due from depository institutions’ of a banking report, and the term securities represents ‘securities’, ‘federal funds sold and reverse repurchase agreements’, and the ‘trading asset account’ of the balance sheets from the banking report at the FDIC.

4 We assumed that the reserve position enhances with the risk-free interest rate although cash has no interest because cash accounts for a small percentage of this subject. The reserve position includes “Cash and Balances Due’ in the bank’s balance sheet. Based on the statistics in the deposit institutions’ balance sheet provided by FDIC, the ‘total noninterest bearing balances’ account for 11.7% and 13.3% of ‘Cash and Balances Due’ in 2017/12/31 and 2018/12/31, respectively. Moreover, the reserve is less than approximately 10% of the bank’s assets. For simplicity, we assumed that the reserve position enhances with the risk-free rate in a bank’s asset model.

5 The details of how to obtain Equation (5) can be found in the Appendix in Duan et al. (1995), where they describe the dynamics of a bank’s asset as containing credit risk and interest rate risk. They project the bank’s asset, which shows the Wiener process credit risk on the interest rate variable to yield $d{V}_t/V_t=\mu dt+{\phi }_{v}d{r}_t+\psi d{W}_t$. A given interest rate process is $d{r}_t$: represents the interest rate risk by stochastic variation against time, and it can adjust the size of the variation of interest risk by multiplying ${\phi }_v$, which is interpreted as the instantaneous interest rate elasticity. Lee and Yu (2002) and Lo et al. (2013) also adopted the model; they assume that the dynamic of the insurer’s assets and insurer’s liability follow the Wiener process of interest rate elasticity to characterize an asset that is sensitive to interest rates risks. Based on Duan et al. (1995), we further consider the interest rate spread and the deposit rate spread on the bank’s liability dynamic as control variables for credit risks.

6 In our scenario analysis in section 3.2, the basic parameter setting is $\text{β}=0.97$ and $\eta =0.8$.

7 The deposit insurance is an insurance contract between a bank and an insurer, and a CDS links the insurer and investors in the credit market. If an insurer takes part of the deposit insurance premium to buy the CDS, then a part of the bank’s risk that the insurer bears is essentially transferred to the CDS market. In this manner, the bank’s total asset risk remains at the same level, but the cash-flow variation of the insurer decreases because the insurer receives less premium and bears less risk of the bank. The CDS sellers (protection seller) receive CDS premiums from insurers and provide protection to insurers on the bank deposits.