Alexander Braun, Marius Fischer and Hato Schmeiser
The purpose of this paper is to show how an insurance company can maximize the policyholder’s utility by setting the level of the interest rate guarantee in line with his…
Abstract
Purpose
The purpose of this paper is to show how an insurance company can maximize the policyholder’s utility by setting the level of the interest rate guarantee in line with his preferences.
Design/methodology/approach
The authors develop a general model of life insurance, taking stochastic interest rates, early default and regular premium payments into account. Furthermore, the authors assume that equity holders must receive risk-adequate returns on their initial equity contribution and that the insurance company has to maintain a solvency restriction.
Findings
The findings show that the optimal level for the interest rate guarantee is in general far below the maximum value typically set by the supervisory authorities and insurance companies.
Originality/value
The authors conclude that the approach of deviating from the maximum interest rate guarantee level given by the regulatory requirements can create additional value for the rational policyholder. In contrast to Schmeiser and Wagner (2014), the second finding shows that the interest rate guarantee embedded in a life insurance product becomes less attractive compared to a pure investment in the underlying asset portfolio to the policyholder when the guarantee level is lowered too far or the contract duration is short. They also refute Schmeiser and Wagner (2014) by showing that the equity capital required by the insurance company increases with the level of the guarantee, even if the insurer is flexible with respect to its asset allocation. The last finding is that a policyholder with higher risk aversion does not generally prefer a higher guarantee level.
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Hato Schmeiser and Daliana Luca
The purpose of this paper is to study how the discretization interval affects the solvency measurement of a property-liability insurance company.
Abstract
Purpose
The purpose of this paper is to study how the discretization interval affects the solvency measurement of a property-liability insurance company.
Design/methodology/approach
Starting with a basic solvency model, the authors study the impact of the discretization interval on risk measures. The analysis considers the sensitivity of the discrepancy between the risk measures in continuous and discrete time to various parameters, such as the asset-to-liability ratio, the characteristics of the asset and liability processes, as well as the correlation between assets and liabilities. Capital requirements for the one-year planning horizon in continuous vs discrete time are reported as well. The purpose is to report the degree to which the deviations in risk measures, due to the different discretization intervals, can be reduced by means of increasing the frequency with which the risk measures are assessed.
Findings
The simulation results suggest that the risk measures of an insurance company are consistently underestimated when assessed on an annual basis (as it is currently done under insurance regulation such as Solvency II). The authors complement the analysis with the capital requirements of an insurance company and conclude that more frequent discretization translates into higher capital requirements for the insurance company. Both the probability of ruin and the expected policyholder deficit (EPD) can be reduced through intermediate financial reports.
Originality/value
The results from our simulation analysis suggest that that the choice of discretization interval has an impact on the risk assessment of an insurance company which uses the probability of ruin and the EPD as risk measures. By assessing the risk measures once a year, both risk measures and the capital requirements are consistently underestimated. Therefore, the recommendation for risk managers is to complement the capital requirements in solvency regulation with sensitivity analyses of the risk measures presented with respect to time discretization. On the one hand, it seems to us that there is value in knowing about the substantial discrepancy between the focused time discrete ruin probability and EPD compared to the continuous version. On the other hand, and if there are no substantial transaction costs associated with more frequent monitoring of solvency figures, a frequent update would be helpful to increase the accuracy of the calculations and reduce the EPD.
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Florian Klein and Hato Schmeiser
The purpose of this paper is to determine optimal pooling strategies from the perspective of an insurer's shareholders underlying a default probability driven premium loading and…
Abstract
Purpose
The purpose of this paper is to determine optimal pooling strategies from the perspective of an insurer's shareholders underlying a default probability driven premium loading and convex price-demand functions.
Design/methodology/approach
The authors use an option pricing framework for normally distributed claims to analyze the net present value for different pooling strategies and contrast multiple risk pools structured as a single legal entity with the case of multiple legal entities. To achieve the net present value maximizing default probability, the insurer adjusts the underlying equity capital.
Findings
The authors show with the theoretical considerations and numerical examples that multiple risk pools with multiple legal entities are optimal if the equity capital must be decreased. An equity capital increase implies that multiple risk pools in a single legal entity are generally optimal. Moreover, a single risk pool for multiple risk classes improves in relation to multiple risk pools with multiple legal entities whenever the standard deviation of the underlying claims increases.
Originality/value
The authors extend previous research on risk pooling by introducing a default probability driven premium loading and a relation between the premium level and demand through a convex price-demand function.
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Hato Schmeiser and Joël Wagner
The purpose of this paper is to analyze what transaction costs are acceptable for customers in different investments. In this study, two life insurance contracts, a mutual fund…
Abstract
Purpose
The purpose of this paper is to analyze what transaction costs are acceptable for customers in different investments. In this study, two life insurance contracts, a mutual fund and a risk-free investment, as alternative investment forms are considered. The first two products under scrutiny are a life insurance investment with a point-to-point capital guarantee and a participating contract with an annual interest rate guarantee and participation in the insurer’s surplus. The policyholder assesses the various investment opportunities using different utility measures. For selected types of risk profiles, the utility position and the investor’s preference for the various investments are assessed. Based on this analysis, the authors study which cost levels can make all of the products equally rewarding for the investor.
Design/methodology/approach
The paper notes the risk-neutral valuation calibration using empirical data utility and performance measurement dynamics underlying: geometric Brownian motion numerical examples via Monte Carlo simulation.
Findings
In the first step, the financial performance of the various saving opportunities under different assumptions of the investor’s utility measurement is studied. In the second step, the authors calculate the level of transaction costs that are allowed in the various products to make all of the investment opportunities equally rewarding from the investor’s point of view. A comparison of these results with transaction costs that are common in the market shows that insurance companies must be careful with respect to the level of transaction costs that they pass on to their customers to provide attractive payoff distributions.
Originality/value
To the best of the authors’ knowledge, their research question – i.e. which transaction costs for life insurance products would be acceptable from the customer’s point of view – has not been studied in the above described context so far.
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Nadine Gatzert and Hato Schmeiser
The purpose of this paper is to provide a detailed analysis of industry loss warranties (ILWs), an alternative risk transfer instrument which has become increasingly popular…
Abstract
Purpose
The purpose of this paper is to provide a detailed analysis of industry loss warranties (ILWs), an alternative risk transfer instrument which has become increasingly popular throughout the last few years.
Design/methodology/approach
The authors first point out key characteristics of ILWs important to investor and cedent, including transaction costs, moral hazard, basis risk, counterparty risk, industry loss index, and regulation. Next, the authors present and discuss the adequacy of actuarial and financial approaches for pricing ILWs, as well as the aspects of basis risk. Finally, drivers of demand and associated models frameworks from the purchaser's viewpoint are studied.
Findings
Financial pricing approaches for ILWs are highly sensitive to input parameters, which is important given the high volatility of the underlying loss index. In addition, the underlying assumption of replicability of the claims is not without problems. Due to their simple and standardized structure and the dependence on a transparent industry loss index, ILWs are low‐barrier products, which can also be offered by hedge funds. In principle, traditional reinsurance contracts are still preferred as a measure of risk transfer, especially since these are widely accepted for solvency capital reduction. However, the main important impact factor for the demand of ILWs from the perspective of market participants, i.e. large diversified reinsurers and hedge funds, is the lower price due to rather low transaction costs and less documentation effort. Hence, ILWs are attractive despite the introduction of basis risk and the still somewhat opaque regulatory environment.
Research limitations/implications
An important issue for future research is how reinsureds deal with the basis risk inherent in ILWs. Another central point is the development of a European industry loss index and the creation of an exchange platform to enable an even higher degree of standardization and a faster processing of transactions.
Originality/value
ILWs feature an industry loss index to be triggered, and, in some cases, a double‐trigger design that includes a company indemnity trigger. ILW contracts belong to the class of alternative risk transfer instruments that have become increasingly popular, especially in the retrocession reinsurance market. There has been no comprehensive analysis of these instruments in academic literature to date. Consequently, the authors believe that this paper provides a high degree of originality.
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Hato Schmeiser, Caroline Siegel and Joël Wagner
The purpose of this paper is to study the risk of misspecifying solvency models for insurance companies.
Abstract
Purpose
The purpose of this paper is to study the risk of misspecifying solvency models for insurance companies.
Design/methodology/approach
Based on a basic solvency model, the authors examine the sensitivity of different risk measures with respect to model misspecification. An analysis considers the effects of introducing stochastic jumps and linear, as well as non‐linear dependencies into the basic setting on the solvency capital requirements, shortfall probability and expected policyholder deficit. Additionally, the authors take a regulatory view and consider the degree to which the deviations in risk measures, due to the different model specifications, can be diminished by means of requiring interim financial reports.
Findings
The simulation results suggest that the sensitivity of solvency capital as a risk measure – as it is in regulatory practice – underestimates the actual misspecification risk that policyholders are exposed to. It is also found that semi‐annual mandatory interim reports can already reduce the model uncertainty faced by a regulator, significantly. This has important implications for the design of risk‐based capital standards and the implementation of internal solvency models.
Originality/value
The results from the Monte Carlo simulation show that changes in the specification of a solvency model have a much greater impact on shortfall probabilities and expected policyholder deficits than they have on capital requirements. The shortfall risk measures react much more sensitively to small changes in the model assumptions, than the capital requirements. This leads us to the conclusion that regulators should not solely rely on capital requirements to monitor the solvency situation of an insurer, but should additionally consider shortfall risk measures. More precisely, an analysis of model risk focusing on the sensitivity of capital requirements will typically underestimate the relevant risk of model misspecification from a policyholder's perspective. Finally, the simulation results suggest that mandatory interim reports on the solvency and financial situation of an insurance company are a powerful tool in order to reduce the model uncertainty faced by regulators.
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Nadine Gatzert and Hato Schmeiser
Definitions of pooling effects in insurance companies may convey the impression that the achieved risk reduction effect will be beneficial for policyholders, since typically lower…
Abstract
Purpose
Definitions of pooling effects in insurance companies may convey the impression that the achieved risk reduction effect will be beneficial for policyholders, since typically lower premiums are paid for the same safety level with an increasing number of insureds, or a higher safety level is achieved for a given premium level for all pool members. However, this view is misleading and the purpose of this paper is to reexamine this apparent merit of pooling from the policyholder's perspective.
Design/methodology/approach
This is achieved by comparing several valuation approaches for the policyholders' claims using different assumptions of the individual policyholder's ability to replicate the contract's cash flows and claims.
Findings
The paper shows that the two considered definitions of risk pooling do not offer insight into the question of whether pooling is actually beneficial for policyholders.
Originality/value
The paper contributes to the literature by extending and combining previous work, focusing on the merits of pooling claims (using the two definitions above) from the policyholder's perspective using different valuation approaches.
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Katja Müller, Hato Schmeiser and Joël Wagner
The purpose of this paper paper is to study effective measures in dealing with the phenomenon of insurance claims’ fraud. In fact, fraud is one of the major industry concerns. It…
Abstract
Purpose
The purpose of this paper paper is to study effective measures in dealing with the phenomenon of insurance claims’ fraud. In fact, fraud is one of the major industry concerns. It occurs in all classes of insurance and accounts for a substantial portion of indemnity payments each year.
Design/methodology/approach
This paper develops a model framework based on a costly state verification setting in which – while policyholders observe the amount of loss privately – the insurance company can decide to audit incoming claims at some cost. The aim is to derive optimal auditing strategies from the insurance company’s perspective while maintaining contract attractiveness to policyholders willing to adhere to the insurance relationship. The possibility for each stakeholder to adapt its behavioral strategy over the course of several periods is taken into account. Using a numerical approach based on Monte Carlo simulations, the impact of different parameterizations on the optimal auditing range by means of a sensitivity analysis is illustrated and analyzed.
Findings
The central outcome of the model is an auditing range which selects those claims which should be subject to verification.
Practical implications
This paper comes to the conclusion that, given some constant cost per audit, it is optimal to verify the accuracy of claims from the mid-value segment. Furthermore, it can be shown that while the option to adapt one’s strategy might be favorable from the insurance company perspective, it has a negative impact on the policyholders’ position. This disproves the common belief that adapting the defrauding strategy with the help of signals from service providers would be advantageous.
Originality/value
This paper extends the stand of literature on costly state verification and gives indications for optimal auditing strategies in industry practice.