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.     

Fair valuation of cliquet-style return guarantees in (homogeneous and) heterogeneous life insurance portfolios

Participating life insurance contracts allow the policyholder to participate in the annual return of a reference portfolio. Additionally, they are often equipped with an annual (cliquet-style) return guarantee. The current low interest rate environment has again refreshed the discussion on risk management and fair valuation of such embedded options. While this problem is typically discussed from the viewpoint of a single contract or a homogeneous* insurance portfolio, contracts are, in practice, managed within a heterogeneous insurance portfolio. Their valuation must then – unlike the case of asset portfolios – take account of portfolio effects: Their premiums are invested in the same reference portfolio; the contracts interact by a joint reserve, individual surrender options and joint default risk of the policy sponsor. Here, we discuss the impact of portfolio effects on the fair valuation of insurance contracts jointly managed in (homogeneous and) heterogeneous life insurance portfolios. First, in a rather general setting, including stochastic interest rates, we consider the case that otherwise homogeneous contracts interact due to the default risk of the policy sponsor. Second, and more importantly, we then also consider the case when policies are allowed to differ in further aspects like the guaranteed rate or time to maturity. We also provide an extensive numerical example for further analysis.     

Assessing the Risk Potential of Premium Payment Options in Participating Life Insurance Contracts

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 increasing 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 annual surplus participation. Next, in addition to the features of the basic contract, a paid-up and resumption option is included in the framework. The valuation process is not based on assumptions about a particular policyholders' exercise strategy but instead assesses the risk potential from the insurer's viewpoint by providing an upper bound for any possible 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.     

A Finite Difference Approach to the Valuation of Path Dependent Life Insurance Liabilities

This paper sets up a model for the valuation of traditional participating life insurance policies. These claims are characterized by their explicit interest rate guarantees and by various embedded option elements, such as bonus and surrender options. Owing to the structure of these contracts, the theory of contingent claims pricing is a particularly well-suited framework for the analysis of their valuation.The eventual benefits (or pay-offs) from the contracts considered crucially depend on the history of returns on the insurance company's assets during the contract period. This path-dependence prohibits the derivation of closed-form valuation formulas but we demonstrate that the dimensionality of the problem can be reduced to allow for the development and implementation of a finite difference algorithm for fast and accurate numerical evaluation of the contracts. We also demonstrate how the fundamental financial model can be extended to allow for mortality risk and we provide a wide range of numerical pricing results.     

An Equilibrium Model of Catastrophe Insurance Futures and Spreads

This article presents a valuation model of futures contracts and derivatives on such contracts, when the underlying delivery value is an insurance index, which follows a stochastic process containing jumps of random claim sizes at random time points of accident occurrence. Applications are made on insurance futures and spreads, a relatively new class of instruments for risk management launched by the Chicago Board of Trade in 1993, anticipated to start in Europe and perhaps also in other parts of the world in the future. The article treats the problem of pricing catastrophe risk, which is priced in the model and not treated as unsystematic risk. Several closed pricing formulas are derived, both for futures contracts and for futures derivatives, such as caps, call options, and spreads. The framework is that of partial equilibrium theory under uncertainty.     

Exotic unit-linked life insurance contracts

This article integrates aspects of traditional insurance with advances in financial economics, yielding proper valuation and premium assessments of insurance benefits linked to various financial assets. Several new types of unit-linked life insurance contracts are discussed, with substantial potential for real-life applications. Compared to usual unit-linked products, these contracts offer added flexibility and/or altered exposure to financial risk for the insured and/or the insurer. The single premiums of these policies are calculated as expectations under a risk-adjusted probability measure (equivalent martingale measure), satisfying no-arbitrage conditions in financial markets.     

Life Insurance Liabilities at Market Value: An Analysis of Insolvency Risk, Bonus Policy, and Regulatory Intervention Rules in a Barrier Option Framework

This article takes a contingent claim approach to the market valuation of equity and liabilities in life insurance companies. A model is presented that explicitly takes into account the following: (i) the holders of life insurance contracts (LICs) have the first claim on the company's assets, whereas equity holders have limited liability; (ii) interest rate guarantees are common elements of LICs; and (iii) LICs according to the so‐called contribution principle are entitled to receive a fair share of any investment surplus. Furthermore, a regulatory mechanism in the form of an intervention rule is built into the model. This mechanism is shown to significantly reduce the insolvency risk of the issued contracts, and it implies that the various claims on the company's assets become more exotic and obtain barrier option properties. Closed valuation formulas are nevertheless derived. Finally, some representative numerical examples illustrate how the model can be used to establish the set of initially fair contracts and to determine the market values of contracts after their inception.     

Market Consistent Embedded Value in der privaten Krankenversicherung

The Market Consistent Embedded Value (MCEV) allows for a principal based valuation of insurance contract portfolios. An important aspect of the MCEV methodology is the possibility to compare different insurance companies. In this paper we introduce the valuation principles with respect to German private health insurance. To this end we first explain the different components of a MCEV. In the following we discuss the relevant aspects of market consistent valuation of German private health insurance and show, how financial options and guarantees of private health insurance contracts influence the shareholder value. In particular we analyze the impact of surplus distribution and the different surrender options of policyholders on the value.     

Insurance Derivatives: A New Asset Class for the Capital Markets and a New Hedging Tool for the Insurance Industry

The number and severity of natural catastrophes has increased dramatically over the last decade. As a result, there is now a shortage of capacity in the property catastrophe insurance industry in the U.S. This article discusses how insurance derivatives, particularly the Chicago Board of Trade's catastrophe options contracts, represent a possible solution to this problem. These new financial instruments enable the capital markets to provide the insurance industry with the reinsurance capacity it needs. The capital markets are willing to perform this role because of the new asset class characteristics of securitized insurance risk: positive excess returns and diversification benefits.
The article also demonstrates how insurance companies can use insurance derivatives such as catastrophe options and catastrophe-linked bonds as effective, low-cost risk management tools. In reviewing the performance of the catastrophe contracts to date, the authors report promising signs of growth and liquidity in these markets.     

Der neue Standard zur bilanziellen Abbildung von Versicherungsverträgen (IFRS 17) – Eine kritische Analyse der Auswirkungen auf die Versicherungsbranche

The new standard for the accounting of insurance contracts (IFRS 17) will entail substantial changes for the insurance industry. In the following article the new standard is critically analyzed. First and foremost the coming valuation model, the so-called building block approach, is presented which will be the basis for all insurance contracts within the scope of IFRS 17. (For certain insurance contracts, especially those with direct participation features, or for less complex or short-term insurance contracts, there are some modifications.) To be more precise, IFRS 17 introduces an enterprise-specific valuation approach that is grounded on the so-called fulfilment value. This fulfilment value is determined by four separate building blocks (fulfilment-cashflow, discount rate, risk margin and contractual service margin), which will be addressed in detail. Finally, major changes in performed accounting practices that insurance enterprises are confronted with and will have to adapt to in their financial statements and accounts are pointed out.     

The analytic valuation of American options

No analytic solution exists for the valuation of American optionswritten on futures contracts and foreign currencies for whichearly exercise may be optimal. This article formulates the Americanoption valuation problem in economically and mathematicallymeaningful ways. This enables us to derive valuation formulasfor American options. The properties associated with the optimalexercise boundary are examined, and a numerical technique toimplement the valuation formulas is presented.     

Creating Customer Value in Participating Life Insurance

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, that is, the guaranteed interest rate and the annual and terminal surplus participation rate. The aim of this article 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. In addition, we derive explicit expressions for a selection of specific cases. Our results suggest that a customer segmentation in this sense, that is, based on the different ways customers evaluate life insurance contracts and embedded investment guarantees while ensuring fair values, is worthwhile for insurance companies as doing so can result in substantial increases in policyholder willingness to pay.     

The Valuation of Options on Futures Contracts

Rational restrictions are derived for the values of American options on futures contracts. For these options, the optimal policy, in general, involves premature exercise. A model is developed for valuing options on futures contracts in a constant interest rate setting. Despite the fact that premature exercise may be optimal, the value of this American feature appears to be small and a European formula due to Black serves as a useful approximation. Finally, a model is developed to value these options in a world with stochastic interest rates. It is shown that the pricing errors caused by ignoring the location of the interest rate (relative to its long-run mean) range from ?5% to 7%, when the current rate is ±200 basis points from its long-run value. The role of interest rate expectations is, therefore, crucial to the valuation. Optimal exercise policies are found from numerical methods for both models.     

Valuing Mortgage Insurance Contracts in Emerging Market Economies

We develop a new option-based method for the valuation of mortgage insurance contracts in closed form in an economy where agents are risk neutral. While the proposed valuation method is general and can be used in any market, it may be particularly useful in emerging market economies where other existing methods may be either inappropriate or are too difficult to implement because of the lack of relevant data. As an application, we price a typical Serbian government-backed mortgage insurance contract.     

Biometric Solvency Risk for Portfolios of General Life Contracts. I. The Single-Life Multiple Decrement Case

Abstract

Solvency II splits life insurance risk into seven risk classes consisting of three biometric risks (mortality risk, longevity risk, and disability/morbidity risk) and four nonbiometric risks (lapse risk, expense risk, revision risk, and catastrophe risk). The best estimate liabilities for the biometric risks are valued with biometric life tables (mortality and disability tables), while those of the nonbiometric risks require alternative valuation methods. The present study is restricted to biometric risks encountered in traditional single-life insurance contracts with multiple causes of decrement. Based on the results of quantitative impact studies, process risk was deemed to be not significant enough to warrant an explicit calculation. It was therefore assumed to be implicitly included in the systematic/parameter risk, resulting in a less complex standard formula. For the purpose of internal models and improved risk management, it appears important to capture separately or simultaneously all risk components of biometric risks. Besides its being of interest for its own sake, this leads to a better understanding of the standard approach and its application extent. Based on a total balance sheet approach we express the liability risk solvency capital of an insurance portfolio as value-at-risk and conditional value-at-risk of the prospective liability risk understood as random present value of future cash flows at a given time. The proposed approach is then applied to determine the biometric solvency capital for a portfolio of general life contracts. Using the conditional mean and variance of a portfolio’s prospective liability risk and a gamma distribution approximation we obtain simple solvency capital formulas as well as corresponding solvency capital ratios. To account for the possibility of systematic/parameter risk, we propose either to shift the biometric life tables or to apply a stochastic biometric model, which allows for random biometric rates. A numerical illustration for a cohort of immediate life annuities in arrears reveals the importance of process risk in the assessment of longevity risk solvency capital.     

A GUIDE TO VALUING EMPLOYEE STOCK OPTIONS WITH A RELOAD FEATURE

At first glance, executive stock options with reload provisions appear to be more complicated than conventional options, and thus the valuation of such options would appear to be more difficult. But, as the authors demonstrate in this article, such reload options provide the employee with a dominant exercise strategy—namely, to exercise the option whenever it is "in-the-money." And the fact that reload options will always be exercised simplifies their valuation by eliminating a major problem—that associated with employee's risk references and uncertain early exercise—in valuing conventional options.     

REAL OPTIONS AND CORPORATE RISK MANAGEMENT

By formulating an integrated strategy that combines the creation and exercise of real options together with other risk management techniques, management can reduce risk and thereby increase firm value. For example, a company that is in a position to delay investing without losing its competitive edge, to abandon a project that becomes unprofitable, or to adjust its operating strategy at low cost can avoid risks and exploit profitable opportunities. But, even when real options are used in this way to limit the risk profile of the firm, financial derivatives can help to hedge any residual risk that would otherwise affect the value of the real options and the overall firm.
An integrated risk management approach requires a careful process of diagnosing a company's risk exposure. First, management must decompose the company's risk exposure to understand the fundamental sources of risk. Second, the company's capacity to bear risk must be determined, which requires an understanding of why individual risks (if left unmanaged) would reduce the value of the firm. Third, different approaches for addressing risk should be explored, ranging from diversification to use of financial derivatives and other contracts to investing in (or exercising) a wide array of real options. Fourth, the firm must properly integrate the different risk management solutions to optimize its strategy.     

An axiomatic approach to the valuation of cash flows

We model a stream of cash flows as an optional stochastic process, and value the cash flows by using a continuous and strictly positive linear functional. By applying a representation theorem from the general theory of stochastic processes we are able to study this valuation principle, as well as properties of the stochastic discount factor it implies. This approach to valuation is useful in the non-presence of a financial market, as is often the case when valuing cash flows arising from insurance contracts and in the application of real options.     

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.