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.     

Capital regulation and deposit insurance

A model of deposit insurance in which the bank closure rule can systematically deviate from the economic insolvency condition used in earlier models is developed. Simulation of that model for plausible parameter values suggests that the failure to close banks on a timely basis has a profound effect in increasing the insurer's liability. The implications of these results for capital regulation are discussed.     

Charter value,minimum bank capital requirement and deposit insurance pricing in equilibrium

This paper shows that leaving insolvent banks with large enough charter values open can be optimal and derives normative bank closure/reorganization policies based on the liquidation value of assets and the charter value. The charter value of a bank is broadly defined as the value that would be foregone due to a closure. Our simulations of risk taking show that an optimal forbearance for an insolvent bank with a large enough charter value alleviates the moral hazard problem. This is because increasing the risk raises the probability of losing the charter value, although it generates a moral hazard gain.     

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 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.     

An analysis of option pricing under systematic consumption risk using GARCH

An issue in the pricing of contingent claims is whether to account for consumption risk. This is relevant for contingent claims on stock indices, such as the FTSE 100 share price index, as investor’s desire for smooth consumption is often used to explain risk premiums on stock market portfolios, but is not used to explain risk premiums on contingent claims themselves. This paper addresses this fundamental question by allowing for consumption in an economy to be correlated with returns. Daily data on the FTSE 100 share price index are used to compare three option pricing models: the Black–Scholes option pricing model, a GARCH (1, 1) model priced under a risk-neutral framework, and a GARCH (1, 1) model priced under systematic consumption risk. The findings are that accounting for systematic consumption risk only provides improved accuracy for in-the-money call options. When the correlation between consumption and returns increases, the model that accounts for consumption risk will produce lower call option prices than observed prices for in-the-money call options. These results combined imply that the potential consumption-related premium in the market for contingent claims is constant in the case of FTSE 100 index options.     

Regulatory competition and forbearance: Evidence from the life insurance industry

Regulatory separation theory indicates that a system with multiple regulators leads to less forbearance and limits producer gains while a model of banking regulation developed by Dell’Ariccia and Marquez (2006) predicts the opposite. Fragmented regulation of the US life insurance industry provides an especially rich environment for testing the effects of regulatory competition. We find positive relations between regulatory competition and profitability measures for this industry, which is consistent with the Dell’Ariccia and Marquez model. Our results have practical implications for the debate over federal versus state regulation of insurance and financial services in the US.     

Stock market momentum, business conditions, and GARCH option pricing models

This paper examines the forecasting performance of GARCH option pricing models from a market momentum perspective, and the possible impacts of financial crises and business conditions are also examined. The empirical results demonstrate that market momentum impacts the forecasting performance of GARCH option pricing models. The EGARCH model performs better under downward market momentum, while the standard GARCH performs better under upward market momentum. In addition, parsimonious models generally outperform richly parameterized ones. The above findings are robust to financial crises, and the results further demonstrate that business conditions influence the forecasting performance of GARCH option pricing models.     

Ownership structure, market discipline, and banks’ risk-taking incentives under deposit insurance

The paper studies the effects of market discipline by creditors and ownership structure on banks’ risk taking in the presence of partial deposit insurance. An agency-cost model explains how the effects of creditor discipline and shareholder control are interdependent, the non-monotonic effect of shareholder control, and the role of leverage. Panel regressions on several hundred banks worldwide 1995-2005 confirm a negative individual risk effect of creditor discipline and the expected convex effect of shareholder control. Increased shareholder control significantly strengthens the negative effect of market discipline on asset risk, but joint effects on overall default risk are limited.     

Capital forbearance and thrifts: Examining the costs of regulatory gambling

This article estimates losses embedded in the capital positions of the 996 FSLIC-insured savings and loan institutions that did not meet capital standards on December 31, 1979. We compare the estimated cost of resolving the insolvencies of these institutions in 1980 with the actual failure-resolution costs for those that were closed by August 31, 1994. Our most conservative estimates, considering only the direct costs associated with delayed closure of only the 372 thrifts that were subsequently closed as independent institutions, show that these costs exceed estimates of the cost of prompt resolution by over 16 billion 1979-dollars.R. P. DeGennaro is an Associate Professor and the 1996–1997 Tennessee Banker's Association Scholar, and J. B. Thomson is Vice President and Director of Financial Services Research.University of TennesseeFederal Reserve Bank of Cleveland     

Private deposit insurance,deposit flows,bank lending,and moral hazard

We examine the role of private unlimited deposit insurance as a complement to federal deposit insurance for deposit flows, bank lending, and moral hazard during a crisis. We find that banks whose deposits are federally and privately fully insured obtain more deposits and expand lending, in contrast to banks whose deposits are only federally insured. We also document that privately insured banks remain prudent in the loan origination process during the subprime crisis. Our results offer novel insights into depositor and bank behavior in the presence of multiple deposit insurance schemes with differential design features. They also illustrate how private sector solutions incentivize prudent bank behavior to strengthen the financial safety net.     

On accurate and provably efficient GARCH option pricing algorithms

The GARCH model has been very successful in capturing the serial correlation of asset return volatilities. As a result, applying the model to options pricing attracts a lot of attention. However, previous tree-based GARCH option pricing algorithms suffer from exponential running time, a cut-off maturity, inaccuracy, or some combination thereof. Specifically, this paper proves that the popular trinomial-tree option pricing algorithms of Ritchken and Trevor (Ritchken, P. and Trevor, R., Pricing options under generalized GARCH and stochastic volatility processes. J. Finance, , 54(1), 377–402.) and Cakici and Topyan (Cakici, N. and Topyan, K., The GARCH option pricing model: a lattice approach. J. Comput. Finance, , 3(4), 71–85.) explode exponentially when the number of partitions per day, n, exceeds a threshold determined by the GARCH parameters. Furthermore, when explosion happens, the tree cannot grow beyond a certain maturity date, making it unable to price derivatives with a longer maturity. As a result, the algorithms must be limited to using small n, which may have accuracy problems. The paper presents an alternative trinomial-tree GARCH option pricing algorithm. This algorithm provably does not have the short-maturity problem. Furthermore, the tree-size growth is guaranteed to be quadratic if n is less than a threshold easily determined by the model parameters. This level of efficiency makes the proposed algorithm practical. The surprising finding for the first time places a tree-based GARCH option pricing algorithm in the same complexity class as binomial trees under the Black–Scholes model. Extensive numerical evaluation is conducted to confirm the analytical results and the numerical accuracy of the proposed algorithm. Of independent interest is a simple and efficient technique to calculate the transition probabilities of a multinomial tree using generating functions.     

Covariance dependent kernels,a Q-affine GARCH for multi-asset option pricing

This paper introduces a class of multivariate GARCH models that extends the existing literature by explicitly modeling correlation dependent pricing kernels. A large subclass admits closed-form recursive solutions for the moment generating function under the risk-neutral measure, which permits efficient pricing of multi-asset options. We perform a full calibration to three bivariate series of index returns and their corresponding volatility indexes in a joint maximum likelihood estimation. The results empirically confirm the presence of correlation dependance in addition to the well known variance dependance in the pricing kernel. The model improves both the overall likelihood and the VIX-implied likelihoods, with a better fitting of marginal distributions, e.g., 15% less error on one-asset option prices. The new degree of freedom is also shown to significantly impact the shape of marginal and joint pricing kernels, and leads to up to 53% differences for out-of-the-money two-asset correlation option prices.     

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.     

Capital, corporate income taxes, and catastrophe insurance

We provide estimates of the equity capital needed and the resulting tax costs incurred when supplying catastrophe insurance/reinsurance using a partial equilibrium model that incorporates a specific loss distribution for US catastrophe losses. After consideration of insurer investment in tax-exempt securities, tax loss carry-back/forward provisions, and personal taxes, our results imply that the tax costs of equity finance alone have a substantial effect on the cost of supplying catastrophe reinsurance. These results help explain a variety of industry developments that reduce tax costs. Also, when coupled with non-tax costs of capital, these results help explain the limited scope of catastrophe insurance/reinsurance.     

Market discipline and deposit insurance

Cross-country evidence presented in this paper suggests that explicit deposit insurance reduces required deposit interest rates, while at the same time it lowers market discipline on bank risk taking. Internationally, deposit insurance schemes vary widely in their coverage, funding, and management. This reflects that there are widely differing views on how deposit insurance should optimally be structured. To inform this debate, we use a newly constructed data set of deposit insurance design features to examine how different design features affect deposit interest rates and market discipline.     

GARCH vs. stochastic volatility: Option pricing and risk management

In this paper we compare the out-of-sample performance of two common extensions of the Black–Scholes option pricing model, namely GARCH and stochastic volatility (SV). We calibrate the three models to intraday FTSE 100 option prices and apply two sets of performance criteria, namely out-of-sample valuation errors and Value-at-Risk (VaR) oriented measures. When we analyze the fit to observed prices, GARCH clearly dominates both SV and the benchmark Black–Scholes model. However, the predictions of the market risk from hypothetical derivative positions show sizable errors. The fit to the realized profits and losses is poor and there are no notable differences between the models. Overall, we therefore observe that the more complex option pricing models can improve on the Black–Scholes methodology only for the purpose of pricing, but not for the VaR forecasts.     

A model of reserves, bank runs, and deposit insurance

A model is presented in which demand deposits backed by fractional currency reserves and public insurance can be beneficial. The model uses Samuelson's pure consumption-loans model. The case for demand deposits, reserves, and deposit insurance rests on costs of illiquidity and incomplete information. The effect of deposit insurance depends upon how, and at what cost, the government meets its insurer's obligation — something which is not specified in practice. It remains possible that demand deposits and deposit insurance are a distortion, and reserve requirements serve only to limit the size of this distortion.     

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.     

An analytic derivation of the cost of deposit insurance and loan guarantees An application of modern option pricing theory

It is not uncommon in the arrangement of a loan to include as part of the financial package a guarantee of the loan by a third party. Examples are guarantees by a parent company of loans made to its subsidiaries or government guarantees of loans made to private corporations. Also included would be guarantees of bank deposits by the Federal Deposit Insurance Corporation. As with other forms of insurance, the issuing of a guarantee imposes a liability or cost on the guarantor. In this paper, a formula is derived to evaluate this cost. The method used is to demonstrate an isomorphic correspondence between loan guarantees and common stock put options, and then to use the well developed theory of option pricing to derive the formula.