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.     

Deposit Insurance, Capital Adequacy Requirements and Interest Rate Dynamics

This paper examines the long run interaction among deposit insurance, bank deposit rates and capital adequacy requirements. Using analysis similar to the price discrimination model of Lott and Roberts (1991) we find that a competitive environment among banks would link the spread between insured and uninsured deposit rates to the size of the insurance premium. We also find that banks that choose to operate at the regulatory minimum capital level, would increase asset risk with increased capital requirements if (1) the implicit interest paid to insured and uninsured depositors is equally sensitive to changes in risk and capital adequacy and (2) the insurance premium is independent of the level of risk and capital adequacy. Under the present risk-based premium structure, asset risk has the potential to decline when the regulatory agency raises capital requirements. Finally, we examine the time series behavior of insured and uninsured interest rates to see if it is consistent with our theoretical model. We find that insured and uninsured rates, along with deposit insurance premiums, are cointegrated series as suggested by our model.     

Risk-based capital standards, deposit insurance, and procyclicality

This article shows that risk-based deposit insurance premiums generate smaller procyclical effects than do risk-based capital requirements. Thus, Basel II's procyclical impact can be reduced by integrating risk-based deposit insurance. If deposit insurance is structured as a moving average of contracts, its procyclical effects can be decreased further. Empirical illustrations of this are presented for 42 banks over the period 1987 to 1996. The results confirm that lengthening the contracts' maturities intertemporally smooths premiums but raises the average premium level needed to compensate the insurer for greater systematic risk. The distribution of risk-based premiums across banks is skewed.     

Interest-risk sensitive deposit insurance premia: Stable ACH estimates

The parameters of interest rate uncertainty are estimated by maximum likelihood for the period 1952–1982, and used to evaluate bank or thrift deposit insurance as a function of duration mismatching, capital/asset ratio, and the recent history of interest rate forecasting errors. Homoskedasticity is overwhelmingly rejected in favor of adaptive conditional heteroskedasticity (ACH). Even after removing this heteroskedasticity, normality gives much lower likelihood than Paretian stable distributions with characteristic exponent in the range 1.614 to 1.714. The conditional deposit insurance values fluctuate by factors in excess of 300 for some duration gaps over the past three decades.     

The pricing of deposit insurance considering bankruptcy costs and closure policies

The paper aims to study the pricing issue of deposit insurance with explicit consideration of bankruptcy costs and closure policies. Full coverage from deposit insurance is imposed by many regulators to stabilize the banking system in the current financial crisis, despite of the potential moral hazard problems. We argue that bankruptcy cost is an important factor in pricing deposit insurance, especially when the insured institution is insolvent. Applying the isomorphic relationship between deposit insurance and put option, we first derive a closed-form solution for the pricing model with bankruptcy costs and closure policies. Then, we modify the barrier option approach to price the deposit insurance in which the bankruptcy cost is set as a function of asset return volatility and more realistic closure policies considering possible forbearance can be accounted for. The properties of the models are supported by numerical simulations and are consistent with the risk-based pricing scheme.     

The shifting value of federal deposit insurance: Implications for reform

This research examines the relationship between the value of federal deposit insurance and bank size. We conclude that the value of deposit insurance has often been greater for the largest bank-holding companies since 1981. This differential is consistent with the notion that largest banks have greater ability to circumvent regulatory and/or market discipline. The source of this differential appears to be due to holding less capital rather than greater asset risk. Insurance costs net of the value of deposit insurance are also relatively lower for the largest banks and have become more so since 1981. These results suggest that recent proposals to improve the deposit insurance system should be evaluated based on their ability to effect even-handed discipline throughout the banking industry to eliminate and forestall further creation of this large institution bias.     

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

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.     

Risk-Based Capital and Credit Insurance Portfolios

This paper analyzes the risk-management practices of a vulnerable credit insurer by studying the effects of time-varying correlations, asset risks and loan maturities on the risk-based capital that backs credit insurance portfolios. Since asset correlations may change over a business cycle, we have analyzed these effects by means of a one-factor Gaussian stochastic model as part of an extended contingent claims analysis. Our results show the need to account for cyclical changes to correlations in the pricing of credit insurance. When compared with the reserve of risk-based capital recommended by the Basel II Internal Ratings-Based (IRB) approach, our model provides a better capital buffer against extreme credit losses, especially in times of recession and/or in a risky business environment. Using a risk-adjusted performance metric (RAPM), we find insurers perform better when insuring relatively short-term loans. We also make several policy recommendations on creating a reserve of risk-based capital to protect against possible loan losses.     

Value-at-risk vs. building block regulation in banking

Existing regulatory capital requirements are often criticized for only being loosely linked to the economic risk of the banks' assets. In view of the attempts of international regulators to introduce more risk sensitive capital requirements, we theoretically examine the effect of specific regulatory capital requirements on the risk-taking behavior of banks. More precisely, we develop a continuous time framework where the banks' choice of asset risk is endogenously determined. We compare regulation based on the Basel I building block approach to value-at-risk or ‘internal model’-based capital requirements with respect to risk taking behavior, deposit insurance liability, and shareholder value. The main findings are: (i) value-at-risk-based capital regulation creates a stronger incentive to reduce asset risk when banks are solvent, (ii) solvent banks that reduce their asset risk reduce the current value of the deposit insurance liability significantly, (iii) under value-at-risk regulation the risk reduction behavior of banks is less sensitive to changes in their investment opportunity set, and (iv) banks' equityholders can benefit from risk-based capital requirements.     

Fairly Priced Deposit Insurance and Bank Charter Policy

The thrust of current deposit insurance reform—risk-based insurance premiums and capital requirements—is an effort to price deposit insurance more fairly. Fairly pricing deposit insurance eliminates inequitable wealth transfers, but it does not lead to an efficient equilibrium. This paper shows that an alternative charter policy results in an efficient separating equilibrium.     

Actuarial pricing of deposit insurance

Using a pricing formula for options on coupon bonds (Jamshidian [1989], El Karoui and Rochet [1990]) we are able to compute the actuarial pricing of deposit insurance for a commercial bank. Our formula takes into account the maturity structure of the bank's balance sheet, as well as market parameters such as the term structure of interest rates and the volatilities of zero coupon bonds. The relation with asset liability management methods is explored.     

The Cost of Deposit Insurance for Privately Held Banks: A Market Comparable Approach

Previous empirical studies that use an option pricing model to estimate deposit insurance costs have been limited to banks that issue publicly traded securities: a bank's security prices are used to infer its risk characteristics. However, if deposit insurance costs are needed for privately held banks, as would be the case under a system of risk-based insurance premiums, then an alternative method is required. This paper presents a “market comparable” approach for valuing private banks' deposit insurance. The approach first uses information on public depository institutions to identify the statistical relationships between a bank's supervisory accounting data and its risk characteristics derived from equity market data. Second, it uses these relationships to predict the risk characteristics of a private depository institution based on its supervisory accounting data. This approach is applied to over 7000 private banks and thrifts to estimate their risk characteristics and their implied risk-neutral and physical probabilities of insolvency. For the vast majority of institutions, these risk characteristics and insolvency probabilities are within a reasonable range.     

Thrift deregulation and federal deposit insurance

The federal insurance funds were designed to cover all insured deposits but lacked a rule specifying how these deposits would be covered if a crisis occurred that swamped either insurance fund. The Congress apparently accepted the argument that strict enforcement and regulation could be used to reduce the probability of failure and thereby avoid large losses to the insurance fund. This flaw in the federal deposit insurance system has permitted insolvent institutions to remain open. The very poor performance of these institutions has skewed aggregate thrift performance in recent years, masking the performance of solvent institutions. A protracted debate has ensued centering on the cost of resolving troubled thrifts and whether healthy thrifts can pay these costs. This debate has drawn attention away from the potential value of the thrift charter.This article was originally presented at the conference, Perspectives on Banking Regulation, Federal Reserve Bank of Cleveland, November 3–4, 1988.     

The use of Hurst and effective return in investing

This study measures the deposit insurance premium under stochastic interest rates for Taiwan's banks by applying the two-step maximum likelihood estimation method. The estimation results suggest that the current premiums—charging 5, 5.5, and 6 basis points per dollar of insured deposits—are too low, but largely reflect the rank orders of the risks of the insured banks. Moreover, the regression results indicate that asset volatility dominates bank size in determining the insurance premium. When the volatility risk is decomposed into two parts, credit risk significantly dominates interest-rate risk. An examination of bank characteristics indicates that privately owned old banks are more likely to have lower levels of credit risk, asset volatility, and deposit insurance premiums than state-owned banks and newly chartered banks.     

Risk in Banking and Capital Regulation

This paper investigates the role of bank capital regulation in risk control. It is known that banks choose portfolios of higher risk because of inefficiently priced deposit insurance. Bank capital regulation is a way to redress this bias toward risk. Utilizing the mean-variance model, the following results are shown: (a) the use of simple capital ratios in regulation is an ineffective means to bound the insolvency risk of banks; (b) as a solution to problems of the capital ratio regulation, the “theoretically correct” risk weights under the risk-based capital plan are explicitly derived; and (c) the “theoretically correct” risk weights are restrictions on asset composition, which alters the optimal portfolio choice of banking firms.     

Bubbles,banks and financial stability

The macroeconomic impact of rational bubbles in a limited commitment economy crucially depends on whether banks or ordinary savers hold the bubble. Banks hold the bubble asset when their leverage is high, when long-term real interest rates are low or when lax supervision allows them to enjoy high deposit insurance subsidies. When banks are the bubble-holders, this amplifies the output boom by reducing loan–deposit rate spreads while the bubble survives but also deepens the recession when the bubble bursts. In contrast, the real impact of bubbles held by ordinary savers is more muted.     

Pitfalls in using market prices to assess the financial condition of depository institutions

In this article we examine the information that stock prices provide about the financial condition of federally insured thrift institutions. In order to assess their financial condition from the different perspectives of stockholders and the federal insurer, we calculate the value of the put option of federal deposit insurance available to thrift institutions. Our results demonstrate that the two perspectives often provide, particularly for unhealthy institutions, quite different views of the financial condition of individual institutions.     

The Bankruptcy Cost of the Life Insurance Industry Under Regulatory Forbearance

Abstract

In this study the Taiwan Insurance Guaranty Fund (TIGF) is introduced to investigate the ex ante assessment insurance guaranty scheme. We study the bankruptcy cost when a financially troubled life insurer is taken over by TIGF. The pricing formula of the fair premium of TIGF incorporating the regulatory forbearance is derived. The embedded Parisian option due to regulatory forbearance on fair premiums is investigated. The numerical results show that leverage ratio, asset volatility, grace period, and intervention criterion influence the default costs. Asset volatility has a significant effect on the default option, while leverage ratio is shown to aggravate the negative influence from the volatility of risky asset. Furthermore, the numerical analysis concludes that the premium for the insurance guaranty fund is risk sensitive and that a risk-based premium scheme could be implemented, hence, to ease the moral hazard.     

The psychological effects on tariff choices for car insurance

Insurance customers increasingly choose between conventional flat-rate car insurance tariffs and innovative usage-based car insurance tariffs such as a pay-per-mile tariff. Usage-based car insurance tariffs require traffic telematics. In this paper, we analyze the decision-making behavior of insurance customers concerning tariff choices as well as the psychological effects. In other service areas, it can be observed that customers often prefer a flat-rate tariff even if their billing rate would be lower on a pay-per-use tariff for a given amount of usage. In study?1, we show that the purchase intention of car insurance tariffs is influenced by psychological effects as well as the customer’s personal experience with the insurance provider and that it is higher for a flat-rate car insurance tariff compared to a pay-per-mile tariff. Customers who have had positive experiences with an insurance provider induce a higher purchase intention for car insurance than customers who have had no experience with an insurance provider. In study?2, we show that the probability of choosing a flat-rate car insurance tariff is higher with increasing monthly kilometers.     

A hierarchical agency model of deposit insurance

This paper develops a hierarchical agency model of deposit insurance. The main purpose of the analysis is to propose a micro-founded model of deposit insurance schemes and study their effects on the behavior of depositors and the monitoring problem for a bank. This paper also characterizes a risk-based premium in equilibrium, and conducts a comparative statics analysis of depositors’ optimal actions. The results supply the basic theoretical foundation for designing deposit insurance schemes. Our findings are consistent with the empirical research on depositor behavior.