An analysis of pricing and basis risk for industry loss warranties

In recent years, industry loss warranties (ILWs) have become increasingly popular in the reinsurance market. The defining feature of ILW contracts is their dependence on an industry loss index. The use of an index reduces moral hazard and generally results in lower prices compared to traditional, purely indemnity-based reinsurance contracts. However, use of the index also introduces basis risk since the industry loss and the reinsured company’s loss are usually not fully correlated. The aim of this paper is to simultaneously examine basis risk and pricing of an indemnity-based industry loss warranty contract, which is done by comparing actuarial and financial pricing approaches for different measures of basis risk. Our numerical results show that modification of the contract parameters to reduce basis risk can either raise or lower prices, depending on the specific parameter choice. For instance, basis risk can be reduced by decreasing the industry loss trigger, which implies higher prices, or by increasing the reinsured company attachment, thus inducing lower prices.     

Reinsurance decisions in life insurance: An empirical test of the risk–return criterion

Recent studies have analyzed optimal reinsurance contracts within the framework of profit maximization and/or risk minimization. This type of framework, however, does not consider reinsurance as a tool for capital management and financing. In the present paper, we consider different proportional reinsurance contracts used in life insurance (viz., quota-share, surplus, and combinations of quota-share and surplus) while taking into account the insurer's capital constraints. The objective is to determine how different reinsurance transactions affect the risk/reward profile of the insurer and whether factors, such as claims severity, premiums, and insurer's risk appetite, influence the choice of a proportional reinsurance coverage. We compare each reinsurance structure based on actual insurance company data, using the risk–return criterion. This criterion determines the type of reinsurance that enables insurer to retain the largest underwriting profits and/or minimize the risk of the retained claims while keeping the insurer's risk appetite constant, assuming a given capital constraint. The results of this study confirm that the choice of reinsurance arrangement depends on many factors, including risk retention levels, premiums, and the variance of the sum insured values (and therefore claims). As such, under heterogeneous insurance portfolio single type of reinsurance arrangement cannot maximize insurer's returns and/or minimize the risk, therefore a combination of different reinsurance coverages should be employed. Hence, future research on optimal risk management choices should consider heterogeneous portfolios while determining the effects of different financial and risk management tools on companies' risk–return profiles.     

Zur Modellierung von Rückversicherungsverträgen in der dynamischen Finanzanalyse

In this paper we study the influence of Gaussian dependencies on the payoff of reinsurance contracts and the resulting effects on a non-life insurer's risk and return profile. To achieve this, we integrate different Gaussian dependencies and reinsurance contracts in a dynamic financial analysis (DFA) framework and conduct numerical tests within a simulation study. Depending on the reinsurance contract and the dependency employed, we find substantial differences in risk assessment for the ruin probability and for the expected policyholder deficit. The results have important implications for regulators and rating agencies that use these risk measures as a foundation for capital standards and ratings. Our results extend the findings of a recent working paper by Eling and Toplek (2008) with a detailed analysis of Gaussian dependencies under different reinsurance contracts.     

Reinsurance premium principles based on weighted loss functions

ABSTRACT

In this paper, we propose new reinsurance premium principles that minimize the expected weighted loss functions and balance the trade-off between the reinsurer's shortfall risk and the insurer's risk exposure in a reinsurance contract. Random weighting factors are introduced in the weighted loss functions so that weighting factors are based on the underlying insurance risks. The resulting reinsurance premiums depend on both the loss covered by the reinsurer and the loss retained by the insurer. The proposed premiums provide new ways for pricing reinsurance contracts and controlling the risks of both the reinsurer and the insurer. As applications of the proposed principles, the modified expectile reinsurance principle and the modified quantile reinsurance principle are introduced and discussed in details. The properties of the new reinsurance premium principles are investigated. Finally, the comparisons between the new reinsurance premium principles and the classical expectile principle, the classical quantile principle, and the risk-adjusted principle are provided.     

Convergence of Insurance and Financial Markets: Hybrid and Securitized Risk-Transfer Solutions

One of the most significant economic developments of the past decade has been the convergence of the financial services industry, particularly the capital markets and (re)insurance sectors. Convergence has been driven by the increase in the frequency and severity of catastrophic risk, market inefficiencies created by (re)insurance underwriting cycles, advances in computing and communications technologies, the emergence of enterprise risk management, and other factors. These developments have led to the development of hybrid insurance/financial instruments that blend elements of financial contracts with traditional reinsurance as well as new financial instruments patterned on asset-backed securities, futures, and options that provide direct access to capital markets. This article provides a survey and overview of the hybrid and pure financial markets instruments and provides new information on the pricing and returns on contracts such as industry loss warranties and Cat bonds.     

Catastrophe Bonds and Reinsurance: The Competitive Effect of Information-Insensitive Triggers

We identify a new benefit of index or parametric triggers. Asymmetric information between reinsurers on an insurer's risk affects competition in the reinsurance market: reinsurers are subject to adverse selection, since only high-risk insurers may find it optimal to change reinsurers. The result is high reinsurance premiums and cross-subsidization of high-risk insurers by low-risk insurers. A contract with a parametric or index trigger (such as a catastrophe bond) is insensitive to information asymmetry and therefore alters the equilibrium in the reinsurance market. Provided that basis risk is not too high, the introduction of contracts with parametric or index triggers provides low-risk insurers with an alternative to reinsurance contracts, and therefore leads to less cross-subsidization in the reinsurance market.     

Analysis of Participating Life Insurance Contracts: A Unification Approach

Fair pricing of embedded options in life insurance contracts is usually conducted by using risk‐neutral valuation. This pricing framework assumes a perfect hedging strategy, which insurance companies can hardly pursue in practice. In this article, we extend the risk‐neutral valuation concept with a risk measurement approach. We accomplish this by first calibrating contract parameters that lead to the same market value using risk‐neutral valuation. We then measure the resulting risk assuming that insurers do not follow perfect hedging strategies. As the relevant risk measure, we use lower partial moments, comparing shortfall probability, expected shortfall, and downside variance. We show that even when contracts have the same market value, the insurance company's risk can vary widely, a finding that allows us to identify key risk drivers for participating life insurance contracts.     

Bestimmung von Deckungsgrenzen bei nicht-proportionalen Rückversicherungsverträgen: Selbstbehalte in Abhängigkeit von Risikoeinstellungen

Risk measures and accordingly risk measurement increasingly gains in importance in economics. Over the past years risk measures were already used at credit and shareholders' equity depositations due to Basel II regulations. The article now introduces a hybrid decision modell and applies it to the reinsurance business. The modell uses a convex combination of risk measures and therewith enables the modelling of risk attitudes. First of all, by doing that, it can be shown, which risk attitude leads to the acceptance of a reinsurance contract, and secondly which deductible an insurer is prepared to undertake. Consequently it is possible to determine the risk attitudes of insurers. In turn, on knowledge of risk attitudes, it becomes possible to generate recommendations of the extent of the deductible at similar reinsurance contracts.     

Enhanced equity-credit modelling for contingent convertibles

Contingent convertible (CoCo) bonds are characterized by forced equity conversion under either an accounting or regulatory trigger. The accounting trigger occurs when the capital ratio of the issuing bank falls below some contractual threshold. Under the regulatory trigger, sometimes called the point-of-non-viability (PONV) trigger, the regulatory authority may enforce equity conversion when the financial health of the bank deteriorates to certain distressed level. In this paper, we propose an equity-credit modelling of the joint process of the stock price and the capital ratio that integrates both a structural approach for the accounting trigger and a reduced-form approach for the PONV trigger of equity conversion. We also construct effective Fortet algorithms and finite difference schemes for numerical pricing of CoCo bonds under various forms of equity conversion pay-off. The pricing properties of CoCo bonds are examined under different assumptions for the state-dependent intensity of the PONV trigger, the contractual specifications and market conditions.     

Analytic option pricing and risk measures under a regime-switching generalized hyperbolic model with an application to equity-linked insurance

Option pricing and managing equity linked insurance (ELI) require the proper modeling of stock return dynamics. Due to the long duration nature of equity-linked insurance products, a stock return model must be able to deal simultaneously with the preceding stylized facts and the impact of market structure changes. In response, this article proposes stock return dynamics that combine Lévy processes in a regime-switching framework. We focus on a non-Gaussian, generalized hyperbolic distribution. We use the most popular linked equity of ELIs, the S&P 500 index, as an example. The empirical study verifies that the proposed regime-switching generalized hyperbolic (RSGH) model gives the best fit to data. In investigating the effects of stock return modeling on pricing and risk management for financial contracts, we derive the characteristic function, embedded option price, and risk measure of equity-linked insurance analytically. More importantly, we demonstrate that the regime-switching generalized hyperbolic (RSGH) model is realistic and can meet the stylistic facts of stock returns, which in turn can be employed in option pricing and risk management decisions.     

Contingent capital with a dual price trigger

This paper evaluates a form of contingent capital for financial institutions that converts from debt to equity if two conditions are met: the firm's stock price is at or below a trigger value and the value of a financial institutions index is also at or below a trigger value. This structure potentially protects financial firms during a crisis, when all are performing badly, but during normal times permits a bank performing badly to go bankrupt. I discuss a number of issues associated with the design of a contingent capital claim, including susceptibility to manipulation, whether conversion should be for a fixed dollar amount of shares or a fixed number of shares; uniqueness of the share price when contingent capital is outstanding; the susceptibility of different contingent capital schemes to different kinds of errors (under and over-capitalization); and the losses likely to be incurred by shareholders upon the imposition of a requirement for contingent capital. I also present an illustrative pricing example.     

Optimal excess-of-loss reinsurance contract with ambiguity aversion in the principal-agent model

ABSTRACT

We discuss an optimal excess-of-loss reinsurance contract in a continuous-time principal-agent framework where the surplus of the insurer (agent/he) is described by a classical Cramér-Lundberg (C-L) model. In addition to reinsurance, the insurer and the reinsurer (principal/she) are both allowed to invest their surpluses into a financial market containing one risk-free asset (e.g. a short-rate account) and one risky asset (e.g. a market index). In this paper, the insurer and the reinsurer are ambiguity averse and have specific modeling risk aversion preferences for the insurance claims (this relates to the jump term in the stochastic models) and the financial market's risk (this encompasses the models' diffusion term). The reinsurer designs a reinsurance contract that maximizes the exponential utility of her terminal wealth under a worst-case scenario which depends on the retention level of the insurer. By employing the dynamic programming approach, we derive the optimal robust reinsurance contract, and the value functions for the reinsurer and the insurer under this contract. In order to provide a more explicit reinsurance contract and to facilitate our quantitative analysis, we discuss the case when the claims follow an exponential distribution; it is then possible to show explicitly the impact of ambiguity aversion on the optimal reinsurance.     

The funding of subsidiaries equity,double leverage and the risk of bank holding companies

Banking groups exploit double leverage when ‘debt is issued by the parent company and the proceeds are invested in subsidiaries as equity’. Financial authorities have frequently raised concerns about the issue of double leverage because this type of intra‐firm financing appears to allow for both the arbitrage of capital and the assumption of risk. This article focuses on the relationship between double leverage and risk‐taking within banking groups. First, we discuss this relationship based on an examination of balance sheet figures. Second, we analyze a large sample of United States Bank Holding Companies (BHCs) from 1990–2014. The results show that BHCs are more prone to risk when they increase their double leverage, namely, when the stake of the parent within subsidiaries is larger than the stand‐alone capital of the parent. This paper's primary implication for policymakers is that the regulators of complex financial entities should more efficiently address the issue of double leverage, thereby limiting the potential negative consequences that arise from corporate instability.     

The Design of Private Reinsurance Contracts

This article examines the effect of asymmetric information on the trading of underwriting risk between insurers and reinsurers and how it is mitigated in a context of long-term relationships. It begins by explaining how information problems affect the efficiency of the allocation of risk between insurers and reinsurers and how long-term implicit contracts allow the inclusion of new information in the pricing of reinsurance coverage. A key feature of these relationships is the reliance on loss-contingent rebates and commissions in the pricing of reinsurance coverage. We argue that when information is revealed only over time, long-term implicit contracts between insurers and reinsurers allow the inclusion of new information into reinsurance pricing. Because of this feature, the allocation of risk between insurers and reinsurers is more efficient. Specifically, such arrangements lead to more reinsurance coverage, higher insurer profits, and lower expected distress in the industry. Journal of Economic Literature Classification Numbers: G22, G13, L15, D81.     

The value of the ‘swap’ feature in equity default swaps

When equity default swap (EDS) contracts were first included in a rated collateralized debt obligation (CDO) deal, some critics doubted the originality of the product. In fact, EDSs are equivalent to already existing binary barrier options on equity, except the premium is not paid upfront, but over time, and conditional on the trigger event not having occurred. Therefore, as opposed to existing options, the buyer of an EDS: (1) postpones payment for protection, and (2) purchases not only protection against a sharp drop in the price of equity, but also the right to cease payments in case the barrier is hit. This paper derives the closed-form pricing formula for equity default swap spreads under the Black–Scholes assumptions, and then quantifies the fraction of the EDS spread actually due to the ‘swap’ feature of the contract for plausible parameter values. It is found that the extra spread due to the swap nature of EDSs is economically significant only for high volatility, high trigger levels, and long time-to-maturity. The impact of interest rates on the value of the ‘swap’ feature is almost exclusively due to the postponement of payments.     

You have more capital than you think

Senior executives typically delegate the responsibility for managing a firm's derivatives portfolio to in-house financial experts and the company's financial advisers. That's a strategic blunder, argues this Nobel laureate, because the inventiveness of modern financial markets makes it possible for companies to double or even triple their capacity to invest in their strategic assets and competencies. Risks fall into two categories: either a company adds value by assuming them on behalf of its shareholders or it does not. By hedging or insuring against non-value-adding risks with derivative securities and contracts, thereby removing them from what the author calls the risk balance sheet, managers can release equity capital for assuming more value-adding risk. This is not just a theoretical possibility. One innovation-the interest rate swap, introduced about 20 years ago-has already enabled the banking industry to dramatically increase its capacity for adding value to each dollar of invested equity capital. With the range of derivative instruments growing, there is no reason why other companies could not similarly remove strategic risks, potentially creating billions of dollars in shareholder value. The possibilities are especially important for private companies that have no access to public equity markets and therefore cannot easily increase their equity capital by issuing more shares. The author describes how derivative contracts of various kinds are already being employed strategically to mitigate or eliminate various risks. He also shows how companies can use the risk balance sheet to identify risks they should not bear directly and to determine how much equity capacity they can release for assuming more value-adding risk.     

World capital markets and Finnish stock returns

The paper explores issues related to time-varying global equity market integration from a Finnish perspective. Finland is an interesting market since profound economic changes and financial deregulation have taken place since the mid-1980s. Using Finnish firm size ranked portfolios and a conditional four-factor asset pricing model, several restrictions on asset behaviour are examined. It is found that a proxy for changing market integration — lagged foreign equity ownership — has a significant impact on the relative importance of local and global risk factors. Significant differences are found between the pricing of shares that were freely-available to all (unrestricted shares) and domestic investors only (restricted shares). Results also suggest that major capital market reforms profoundly affect the degree of market integration, but local risk factors do not become redundant.     

Lessons from the Financial Crisis on Risk and Capital Management: The Case of Insurance Companies

This article proposes that risk management be viewed as an integral part of the corporate value‐creation process— one in which the concept of economic capital can provide companies with the financial cushion and confidence to carry out their strategic plans. Using the case of insurance and reinsurance companies, the authors discuss three main ways that the integration of risk and capital management creates value:

• 1 strengthening solvency (by limiting the probability of financial distress);
• 2 increasing prospects for profitable growth (by preserving access to capital during post‐loss periods); and
• 3 improving transparency (by increasing the “information content” or “signaling power” of reported earnings).

Insurers can manage solvency risk by using Enterprise Risk Management (ERM) models to limit the probability of financial distress to levels consistent with the firm's specified risk tolerance. While ERM models are effective in managing “known” risks, we discuss three practices widely used in the insurance industry to manage “unknown” and “unknowable” risks using the logic of real options—slack, mutualization, and incomplete contracts. Second, risk management can create value by securing sources of capital that, like contingent capital, can be used to fund profitable growth opportunities that tend to arise in periods following large losses. Finally, the authors argue that risk management can raise the confidence of investors in their estimates of future growth by removing the “noise” in earnings that comes from bearing non‐core risks, thereby making current earnings a more reliable guide to future earnings. In support of this possibility, the authors provide evidence showing that, for a given level of reported return on equity (ROE), (re)insurers with more stable ROEs have higher price‐to‐book ratios, suggesting investors' willingness to pay a premium for the stability provided by risk management.     

Risk‐Adjusted Measures of Value Creation in Financial Institutions

Abstract Many financial institutions assess portfolio decisions using RAROC, the ratio of expected return to risk (or ‘economic’) capital. We use asset pricing theory to determine the appropriate hurdle rate, finding that this varies with the skewness of asset returns. We quantify this discrepancy under a range of assumptions showing that the RAROC hurdle rate differs substantially, being higher by a factor of five or more for equity which has a right skew compared to debt which has a pronounced left skew, and also between different qualities of debt exposure. We discuss implications for both financial institution risk management and supervision.     

International Insurance Society Roundtable on Risk Management After the Crisis

In this roundtable, an adviser to several central banks and founding member of the Group of 30 discusses regulatory reform and corporate risk management strategies with senior executives from three of the world's largest insurance companies. Much of the discussion attempts to explain why insurance and reinsurance companies have proven less vulnerable to the crisis than commercial and investment banks. Part of the explanation has to do with their financial conservatism, which is attributed to a habitual tendency to decision‐making that gives heavy weight to long‐term probabilities and risks. But along with this “actuarial” cast of mind is a growing willingness to accept and make use of risk‐based capital requirements—a decision‐making framework that is, in some respects, in conflict with the accounting and regulatory capital conventions that still prevail in the industry. In particular, “Solvency II”—the risk‐based capital guidelines that are set for adoption in 2012 by insurers in the European Union—is held up as a possible model for global use.