Deposit Insurance Pricing Model Research Articles

A Price Formula of Deposit Insurance Based on Merton Deposit Insurance Pricing Model

A reasonable deposit insurance price can effectively not only reduce the adverse selection problem, but plays an important role in reducing the systemic risk of Banks. By studying the heteroscedasticity of bank asset returns and the sequence of bank debt repayment, this paper deduces the closed form deposit insurance price formula, which further improves and expands Merton's deposit insurance pricing model.

An Optimal Investment Strategy and Multiperiod Deposit Insurance Pricing Model for Commercial Banks

We employ the method of stochastic optimal control to derive the optimal investment strategy for maximizing an expected exponential utility of a commercial bank’s capital at some future date T>0. In addition, we derive a multiperiod deposit insurance (DI) pricing model that incorporates the explicit solution of the optimal control problem and an asset value reset rule comparable to the typical practice of insolvency resolution by insuring agencies. By way of numerical simulations, we study the effects of changes in the DI coverage horizon, the risk associated with the asset portfolio of the bank, and the bank’s initial leverage level (deposit-to-asset ratio) on the DI premium while the optimal investment strategy is followed.

Systematic risk and deposit insurance pricing

PurposeThe purpose of this paper is to alleviate the moral hazard problem created by deposit insurance and therefore develop a deposit insurance pricing model explicitly considering systematic risk.Design/methodology/approachUsing the market model, the authors introduce the systematic risk component consisting of market risk and beta risk. A closed-form solution for the authors’ pricing model is derived based on the option pricing framework.FindingsCompared with the authors’, the pricing model that ignores systematic risk underestimates deposit insurance premium, and cannot cover the excessive loss created by systematic risk. To examine the effect of the systematic risk component on the deposit insurance premiums estimated by the authors’ model, this paper also provides empirical evidence from China by regression analysis. The results demonstrate that, in addition to the individual failure risk, the systematic risk component is properly priced and explicitly reflected in the authors’ model.Research limitations/implicationsMore risk factors such as liquidity risk should be introduced in the pricing of deposit insurance.Practical implicationsDeposit insurance premiums estimated by the authors’ model can alleviate the moral hazard problem that banks have an incentive to take on excessive systematic risk, because substantial higher insurance premiums would be charged in doing so.Originality/valueApplying the option pricing theory and market model, this paper develops a deposit insurance pricing model with explicit consideration of systematic risk. The systematic risk component contains not only the market volatility but also the sensitivity of market risk.

基于几何分数布朗运动的溢额再保险存款保险定价

在假定银行资产服从几何分数布朗运动的前提下，建立了溢额再保险存款保险定价模型，并利用保险精算方法推导出存款保险定价公式。最后选取了我国四大国有银行进行了实证分析，结果表明存款保险费率与银行资产波动率呈现一定的正相关性，且再保险费率均低于原保险费率。因此，所建立的基于几何分数布朗运动的溢额再保险的存款保险定价模型更能反映实际。 Under the assumption of bank assets subject to geometric fractional Brownian motion, the deposit insurance pricing model of excess reinsurance is established. And the deposit insurance pricing formula is derived with actuarial methods. Finally, China’s four major state-owned banks’ empirical analysis shows that the deposit insurance rates and the volatility of bank assets showed some positive correlation, and the reinsurance premium rates were lower than the original. Therefore, the established deposit insurance pricing model of excess reinsurance based on geometric frac-tional Brownian motion is better to reflect reality.

The pricing of deposit insurance in the presence of systematic risk

Based on the Merton (1977) put option framework, we develop a deposit insurance pricing model that incorporates asset correlations, a measurement for the systematic risk of a bank, to account for the risk of joint bank failures. Estimates from our model suggest that actuarially fair risk-based deposit insurance that considers only individual bank failure risk is underpriced, leaving insurance providers exposed to net losses. Our estimates also capture the size premium where big banks are priced with higher deposit insurance than small banks. This result is particularly relevant to the current regulatory concerns on big banks that are too-big-to-fail. Above all, our approach provides a unifying framework for integrating risk-based deposit insurance with risk-based Basel capital requirements.

APPLYING A TWO-STEP MAXIMUM LIKELIHOOD METHOD TO EXAMINE THE DEPOSIT INSURANCE PROGRAM OF TAIWAN

This paper examines the deposit insurance program of Taiwan. We adopt Duan et al. [4]'s deposit insurance pricing model, and estimate the deposit insurance premium by the Duan and Simonato two-step maximum likelihood method [5]. Our results show that the maximum likelihood estimates for the deposit insurance premium are considerably higher than the official rates currently charged by the Central Deposit Insurance Corporation (CDIC), the deposit insuring agency of Taiwan, indicating that the CDIC deposit insurance program appears to hand out a substantial subsidy to the banks in Taiwan. Our results also show that the CDIC in fact grants too much capital forbearance to the banks, and that the semiannual bank audits currently mandated by the CDIC are in fact much less frequent than our estimated values. These findings may also explain why the estimated rates for the deposit insurance premium are much higher than the current CDIC rates.

Maximum likelihood estimation of deposit insurance value with interest rate risk

This paper develops a maximum likelihood estimation method for the deposit insurance pricing model of Duan, Moreau and Sealey (DMS) [J. Banking Financ. 19 (1995) 1091.]. A sample of 10 US banks is used to illustrate the estimation method. Our results are then compared to those obtained with the modified Ronn–Verma method used in DMS. Our findings reveal that the maximum likelihood method yields estimates for the deposit insurance value much larger than the ones based on the modified Ronn–Verma method. We conduct a Monte Carlo study to ascertain the performance of the maximum likelihood estimation method. The simulation results are clearly in favor of our proposed method.

Capital standard, forbearance and deposit insurance pricing under GARCH

We propose a multiperiod deposit insurance pricing model that simultaneously incorporates the capital standard and the possibility of forbearance. The model employs the recently developed GARCH option pricing technique in determining the deposit insurance value. Our model offers two distinctive advantages. First, it explicitly considers the implications of the strict enforcement on capital standard as stipulated in FDIC Improvement Act of 1991. Second, the use of the GARCH model allows us to capture many robust features exhibited by financial asset returns. By the GARCH option pricing theory, the value of a contingent claim is a function of the asset risk premium. This unique feature is found to be prominent in determining the bank's deposit insurance value. We also examine the effects of capital forbearance and moral hazard behavior in this multiperiod deposit insurance setting.

Measuring fair capital adequacy holdings for banks: The case of Taiwan

An option-theoretical framework was employed to solve the level of capital at which Taiwan's deposit insurer would just break even in guaranteeing the deposits of individual banks. The method is applied to ten banks in Taiwan yearly from 1985 to 1992. Asset value and volatility parameters were estimated using the maximum likelihood method via market-based equity data. These critical values were then applied as inputs in Merton's (7) deposit insurance pricing model towards yielding the fair levels of capital adequacy for each individual bank. The estimates showed that, except for in 1989, most of the sample banks were inadequately capitalized. Additionally, estimates of adequate levels of capital for the four commercial banks were found to generally exceed 10 billion NT (US$ 400 million). This finding indicates that the 10 billion NT initial capital requirement now imposed on new commercial banks, though generally perceived as high by the public, may actually not be adequate.

Assessing the cost of Taiwan's deposit insurance

This article uses Merton's deposit insurance pricing model to analyze ten depository institutions in Taiwan (Merton, R., 1977, Journal of Banking and Finance, 1, 3–11). A market-value-based maximum likelihood estimation method developed by Duan (Duan, J.-C., 1994, Mathematical Finance, 4, 155–167) is employed to compute the inputs needed for Merton's formula. Our findings indicate that these institutions were by and large heavily subsidized by the deposit insuring agency. By comparing the estimates obtained using the Ronn and Verma (1986) method, our results also raise a question as to the appropriateness of the Ronn and Verma method for deposit insurance pricing.