The aim of this article is to identify fair equity-premium combinations for non-life insurers that satisfy solvency capital requirements imposed by regulatory authorities. In particular, we compare "target capital" derived using the "value at risk" concept as planned for Solvency II in the European Union with the "tail value at risk" concept as required by the Swiss Solvency Test. The model framework uses Merton's jump-diffusion process for the market value of liabilities and a geometric Brownian motion for the asset process; valuation is conducted using option pricing theory. In this setting, we study the impact of model parameters and corporate taxation on fair pricing, solvency capital requirements, and shortfall probability for different safety levels measured by the default put option value. We show that even though corporate taxes can have a substantial impact on pricing and capital structure, they do not affect capital requirements if the safety level is retained before and after taxation.
Most life insurance contracts embed the right to stop premium payments during the term of the contract (paid-up option). Thereby, the contract is not terminated but continues with reduced benefits and often provides the right to resume premium payments later,
thus reincreasing the previously reduced benefits (resumption option). In our analysis, we start with a basic contract with two standard options, namely, an interest-rate guarantee and cliquet-style annual surplus participation. Next, we include, in addition to the
features of the basic contract, a paid-up and resumption option in the framework. We do not base our pricing on assumptions about particular exercise strategies, but instead assess the risk potential by providing an upper bound to the option price which is independent
of the policyholder's exercise behavior. This approach provides important information to the insurer about the potential hazard of offering the paid-up and resumption option. Further, the approach allows an analysis of the impact of guaranteed interest rate, annual surplus participation, and investment volatility on the values of the premium payment options.
Fair pricing of embedded options in life insurance contracts is usually conducted by using the appropriate concept of risk-neutral valuation. This concept assumes a perfect hedging strategy, which insurance companies can hardly pursue in practice. In this paper, 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 shortfall 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.
Common features in life insurance contracts are an interest rate guarantee and policyholder participation in the returns of insurers' reference portfolio, which can be of substantial value. The aim of this paper is to analyze the model risk involved in pricing and risk assessment that arises from the process specification of the reference portfolio. This is, in general, the most important source of model risk and is analyzed by comparing results from the standard Black-Scholes setting with a Lévy-type model based on a Normal Inverse Gaussian process. We focus on the dependence of the insurer's insolvency risk associated with fair contracts on the specification of the underlying asset process using lower partial moments. We show that a misspecification of the underlying stochastic asset model may not only result in serious mispricing, but also lead to an inadequate assessment of insurers' shortfall risk. Model risk can thus imply substantial solvency risk for insurance companies.
The value of a life insurance contract may differ depending on whether it is looked
at from the customer's point of view or that of the insurance company. We assume
that the insurer is able to replicate the life insurance contract's cash flows via assets
traded on the capital market and can hence apply risk-neutral valuation techniques.
The policyholder, on the other hand, will take risk preferences and diversification
opportunities into account when placing a value on that same contract. Customer
value is represented by policyholder willingness to pay and depends on the contract
parameters, i.e., the guaranteed interest rate and the annual and terminal surplus
participation rate. The aim of this paper is to analyze and compare these two perspectives.
In particular, we identify contract parameter combinations that--while
keeping the contract value fixed for the insurer--maximize customer value. Our
results suggest that it would be very worthwhile for insurance companies to engage
in customer segmentation based on the different ways customers evaluate life insurance contracts and embedded investment guarantees as doing so could result in
substantial increases in policyholder willingness to pay.
