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.     

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.     

Risk management opportunities in auto insurance: A focus on the value of vehicles

Ratemaking and risk-based pricing revolve around the value at risk, involving a tendency of higher values implying higher premiums. Traditionally, vehicle values are set at “list price” and depreciate over time on a one-size-fits-all factor model. If values change over time, so should premiums, but a single factor table that only goes downward to flat is out of sorts with today. In today's transactional data streams, vehicle features, and values can be easily observed—of note, a shift in product mix that has more options and higher retained values creates a gap in actual versus traditionally expected insurance values. This gap most acutely appears at the vehicle “as built” level, which is more granular than current segmentation levels of insurance ratemaking vehicle valuation analysis. The result is leaving companies to simply raise base rates universally until they can adapt more flexible price-to-value methods at an “as built” price accuracy sophistication level.     

Addressing insurance price discrimination in an era of diversity,equity, and inclusion

The early 2020s diversity, equity, and inclusion movement has prompted debate about banning the use of suspect insurance pricing variables because they discriminate against protected classes, such as gender. This paper demonstrates how banning an insurance pricing variable currently used in insurance pricing models can result in regulatory adverse selection if the ban heterogeneously combines policyowners with different expected losses into the same risk class, contrary to risk-based pricing. The paper begins by describing several recent regulatory and judicial decisions to ban insurance pricing variables. It next describes the process used by insurers to set insurance prices, followed by a discussion of applicable insurance discrimination laws. Using a simple risk aversion model, the paper next examines whether a ban on gender-based auto insurance pricing in California in 2019 results in regulatory adverse selection. The paper concludes by describing possible alternative pricing variables available to auto insurers if gender-based pricing is banned.     

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.     

Risk selection in the London political risk insurance market: the role of tacit knowledge,trust and heuristics

This study demonstrates that the basis of decision-making and risk selection in the London Political Risk Insurance (PRI) market is a combination of Art and Science with such factors as trust and reputation playing an important role. The study breaks new ground by uncovering and examining different methods and strategies of political risk underwriting employed in the insurance market, which does not rely on statistical tools as seen in more traditional insurance types. Adopting a grounded theory approach, the data was generated through 14 semi-structured and unstructured interviews conducted with PRI experts from five PRI companies and two leading political risk broking houses. The data also included documentation reviews and observations.     

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.     

Estimating portfolio risk for tail risk protection strategies

We forecast portfolio risk for managing dynamic tail risk protection strategies, based on extreme value theory, expectile regression, copula‐GARCH and dynamic generalized autoregressive score models. Utilizing a loss function that overcomes the lack of elicitability for expected shortfall, we propose a novel expected shortfall (and value‐at‐risk) forecast combination approach, which dominates simple and sophisticated standalone models as well as a simple average combination approach in modeling the tail of the portfolio return distribution. While the associated dynamic risk targeting or portfolio insurance strategies provide effective downside protection, the latter strategies suffer less from inferior risk forecasts, given the defensive portfolio insurance mechanics.     

Valuing catastrophe derivatives under limited diversification: A stochastic dominance approach

We present a new approach to the pricing of catastrophe event (CAT) derivatives that does not assume a fully diversifiable event risk. Instead, we assume that the event occurrence and intensity affect the return of the market portfolio of an agent that trades in the event derivatives. Based on this approach, we derive values for a CAT option and a reinsurance contract on an insurer’s assets using recent results from the option pricing literature. We show that the assumption of unsystematic event risk seriously underprices the CAT option. Last, we present numerical results for our derivatives using real data from hurricane landings in Florida.     

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.     

Optimal investment of an insurer with regime-switching and risk constraint

We investigate an optimal investment problem of an insurance company in the presence of risk constraint and regime-switching using a game theoretic approach. A dynamic risk constraint is considered where we constrain the uncertainty aversion to the ‘true’ model for financial risk at a given level. We describe the surplus of an insurance company using a general jump process, namely, a Markov-modulated random measure. The insurance company invests the surplus in a risky financial asset whose dynamics are modeled by a regime-switching geometric Brownian motion. To incorporate model uncertainty, we consider a robust approach, where a family of probability measures is cosidered and the insurance company maximizes the expected utility of terminal wealth in the ‘worst-case’ probability scenario. The optimal investment problem is then formulated as a constrained two-player, zero-sum, stochastic differential game between the insurance company and the market. Different from the other works in the literature, our technique is to transform the problem into a deterministic differential game first, in order to obtain the optimal strategy of the game problem explicitly.     

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.     

The Perfect Storm: Hurricanes, Insurance, and Regulation

The intense hurricane seasons of 2004 and 2005 caused considerable instability in property insurance markets in coastal states with the greatest problems occurring in Florida and the Southeast. Insurers have substantially raised rates and decreased their exposures. While no severe hurricanes struck the United States in 2006 and 2007, market pressures remain strong given the high risk still facing coastal states. These developments generate considerable concern and controversy among various stakeholder groups. Government responses have varied. In Florida, political pressures prompted a wave of legislation and regulations to expand government underwriting and subsidization of hurricane risk and constrain insurers' rates and market adjustments. Other states' actions seem more moderate. In this context, it is important to understand how property insurance markets have been changing and governments have been responding to increased catastrophe risk. This article examines important market developments and evaluates associated government policies. We comment on how regulation is affecting the equilibration of insurance markets and offer opinions on policies that are helpful and harmful.     

A risk-based approach for pricing American options under a generalized Markov regime-switching model

This paper considers a risk-based approach for pricing an American contingent claim in an incomplete market described by a continuous-time, Markov, regime-switching jump-diffusion model. We formulate the valuation problem as a stochastic differential game and use dynamic programming. Verification theorems for the Hamilton–Jacobi–Bellman–Issacs (HJBI) variational inequalities of the games are used to determine the seller's and buyer's prices and optimal exercise strategies.     

Capital and risk in property-liability insurance markets

This paper investigates the capital and portfolio risk decisions of property-liability insurance firms. A theoretical model based on option pricing theory is developed which predicts a positive relationship between insurer capital and risk, as firms balance these two factors to achieve their desired overall insolvency risk. The implications of the model are then tested empirically using a simultaneous equations methodology. The results support the predictions of the model. They also provide evidence that managerial incentives play a role in determining capital and risk in insurance markets. The findings have significant implications for insurance solvency regulation.     

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.     

Insurance demand in the presence of loss-dependent background risk

We analyze insurance demand when insurable losses come with an uninsurable zero-mean background risk that increases in the loss size. If the individual is risk vulnerable, loss-dependent background risk triggers a precautionary insurance motive and increases optimal insurance demand. Prudence alone is sufficient for insurance demand to increase in two cases: the case of fair insurance and the case where the smallest possible loss exceeds a certain threshold value (referred to as the large loss case). We derive conditions under which insurance demand increases or decreases in initial wealth. In the large loss case, prudence determines whether changes in the background risk lead to more insurance demand. We generalize this result to arbitrary loss distributions and find conditions based on decreasing third-degree Ross risk aversion, Arrow–Pratt risk aversion, and Arrow–Pratt temperance.     

Risk perception and risk management in the Middle East market: theory and practice of multinational enterprises in Saudi Arabia

This exploratory study investigates the risk perception and risk management strategies of Western multinational enterprises in the Middle East. A sample of 49 German companies operating in Saudi Arabia provides the empirical setting for this research. The study reveals that cultural risk is assessed as more important in the business environment than political, financial, and economic risk. The most critical risk factors are not sufficiently included in the methodology of country risk measures, which are often used as a source for country‐specific risk information. In terms of risk management strategies, participating firms use mostly informal approaches rather than structured hedging or insurance products. Furthermore, we find that firm size has implications on the perception of some risk factors and for the level of risk management sophistication.     

背景风险对保险需求的影响——基于中国健康保险市场的实证研究

保险需求理论研究表明,不可保的背景风险会增加投保人对可保风险的保险需求。本文把2003年发生的SARS看作一次自然实验,来检验背景风险对保险需求的影响。本文用我国健康保险市场的时间序列数据,通过邹-检验和时间序列结构突变检验方法,对存在背景风险时的保险需求理论进行实证研究。研究发现,背景风险会增加投保人对可保风险的保险需求,但这种影响只具有短期效应。     

Improving risk classification and ratemaking using mixture-of-experts models with random effects

In the underwriting and pricing of nonlife insurance products, it is essential for the insurer to utilize both policyholder information and claim history to ensure profitability and proper risk management. In this paper, we apply a flexible regression model with random effects, called the Mixed Logit-weighted Reduced Mixture-of-Experts, which leverages both policyholder information and their claim history, to categorize policyholders into groups with similar risk profiles, and to determine a premium that accurately captures the unobserved risks. Estimates of model parameters and the posterior distribution of random effects can be obtained by a stochastic variational algorithm, which is numerically efficient and scalable to large insurance portfolios. Our proposed framework is shown to outperform the classical benchmark models (Logistic and Lognormal GL(M)M) in terms of goodness-of-fit to data, while offering intuitive and interpretable characterization of policyholders' risk profiles to adequately reflect their claim history.