Peter Løchte Jørgensen

Fair Valuation of Life Insurance Liabilities: The Impact of Interest Rate Guarantees, Surrender Options, and Bonus Policies

The paper analyzes one of the most common life insurance products the so-called participariflg (or with pro@) policy. This type of contract stands in contrast to UnitLinked (UL) products in that interest is credited to the policy periodically according to some mechanism which smoothes past returns on the life insurance company’s (LIC) assets. As is the case for UL products, the participating policies are typically equipped with an interest rate guarantee and possibly also an option to surmnder (sell-back) the policy to the LIC before maturity. The paper shows that the typical participating policy can be decomposed into a risk free bond element, a bonus option, and a surrender option. A dynamic model is constructed in which these elements can be valued separately using contingent claims analysis. The impact of various bonus policies and various levels of the guaranteed interest rate is analyzed numerically. We find that values of participating policies are highly sensitive to the bonus policy, that surrender options can be quite valuable, and that LIC solvency can be quickly jeopardized if earning opportunities deteriorate in a situation where bonus reserves are low and promised returns are high. JEL Classification Codes: G13, G22, and G23. Subject/Insurance Branche Codes: IMlO and IEOl.

Valuation of Early Exercisable Interest Rate Guarantees

Interest rate guarantees are important elements of many financial contracts offered in todays financial markets. For example, life insurance policies often contain an explicit interest rate guarantee that ensures the investor a certain minimum return during some specified period. Sometimes the interest rate guarantee is of American type in the sense that it applies for a period of time chosen by the investor. In life insurance contracts this is labeled the surrender feature. This article analyzes the valuation of American or early exercisable interest rate guarantees. We draw on some recent results on American option pricing theory to obtain analytic formulas for the interest rate guarantees. The theoretic results are accompanied by numerical examples, and comparisons to European type guarantees are made.

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 companys 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.

On accounting standards and fair valuation of life insurance and pension liabilities

The actuarial profession is increasingly teaming up with financial economists for a fruitful cooperation on the proper valuation of life insurance and pension (L&P) liabilities. This has been a natural consequence of a recent sharply increased focus on market values in financial reports of L&P companies from regulators, standard setters, the financial press, stakeholders, and others with an interest in the L&P business. This article provides a financial economists point of view on recent developments in relation to the fair valuation of L&P liabilities. The role of accounting standards and the background for the international harmonization in this field are first discussed. We then review and explain the concept of fair value and provide a general view on appropriate techniques for estimating fair values of L&P liabilities in accordance with the definition of the concept. The paper also contains a section which briefly reviews recent and quite innovative regulatory initiatives in relation to market value reporting in the Danish market for life and pension insurance.

Lognormal Approximation of Complex Path-dependent Pension Scheme Payoffs

This paper analyzes an explicit return smoothing mechanism which has recently been introduced as part of a new type of pension savings contract that has been offered by Danish life insurers. We establish the payoff function implied by the return smoothing mechanism and show that its probabilistic properties are accurately approximated by a suitably adapted lognormal distribution. The quality of the lognormal approximation is explored via a range of simulation-based numerical experiments, and we point to several other potential practical applications of the papers theoretical results.Abstract This paper analyzes an explicit return smoothing mechanism which has recently been introduced as part of a new type of pension savings contract that has been offered by Danish life insurers. We establish the payoff function implied by the return smoothing mechanism and show that its probabilistic properties are accurately approximated by a suitably adapted lognormal distribution. The quality of the lognormal approximation is explored via a range of simulation-based numerical experiments, and we point to several other potential practical applications of the papers theoretical results.

Time Charters with Purchase Options in Shipping: Valuation and Risk Management

The paper studies the valuation and optimal management of Time Charters with Purchase Options (T/C-POPs) which is a specific type of asset lease with embedded options that is common in shipping markets. T/C-POPs are economically significant and sometimes account for more than half of the stock market value of listed shipping companies. The main source of risk in markets for maritime transportation is the freight rate, and we therefore specify a single-factor continuous time model for the dynamic evolution of freight rates which allows us to price a wide variety of freight rate related derivatives including various forms of T/C-POPs using contingent claims valuation techniques. Our model allows for the derivation of closed valuation formulas for some simple freight rate derivatives while the more complex ones are analyzed using numerical (finite difference) procedures. We accompany our theoretical results with illustrative numerical examples as we proceed

Optimal Investment in Structured Bonds

Structured investment vehicles for retail customers have become increasingly prevalent, and also increasingly complex. Yet numerous articles have shown that many popular structures offer rather poor performance for the buyer, relative to the expected payoff and to the cost of producing that payoff with a combination of simpler derivative contracts. Retail investors seem to like payoffs resembling that of a protectiveput strategy very much, with exposure on the upside but limited risk of loss on the downside. Why should they be willing to pay more for such products than they are worth? In this article, Jessen and Jørgensen show that such structured products can make sense for an investor with an ordinary utility function if the diversification value of exposure to the underlying index is great enough and the structured product is the only way they can obtain exposure to that index.

A Comparison of Three Different Pension Savings Products with Special Emphasis on the Payout Phase

Abstract The purpose of this article is to illustrate how the pension benefits a pension saver will (expect to) receive will depend on the type of pension scheme chosen. We compare three widely different pension savings products: the “traditional” with-profits scheme involving bonus entitlement (average interest rate product), a market-based Unit Link scheme and, finally, a formula based smoothed investment-linked annuity scheme – TimePension in short – which is on many points a cross between the two prior-mentioned types of savings products. The three product types mentioned above have been analysed in previous literature, but those comparisons were based almost entirely on the values of pension savings accounts at the expiry of the accumulation period. This article will include the payout phase (decumulation phase) in the analysis, enabling us to analyse the size of paid-out pension benefits themselves as well as the possibilities of adjusting these benefits periodically. Compared to earlier articles, we have also improved the underlying model for the uncertainty of the underlying financial market. The article demonstrates that expected pension benefits from the three schemes are an increasing function of the allocation to shares in the underlying investment portfolios. TimePension involves the highest allocation to shares and therefore offers, on average, the highest pension benefits, followed by the Unit Link scheme. In the third and last place comes the traditional with-profits scheme, which has a relatively low allocation to shares, but which, in return, also provides relatively safe and stable pension benefits. We also show, however, that the stability of pension benefits from a TimePension scheme is completely level with the stability of benefits from the traditional scheme. Unit Link-based pension benefits, on the other hand, vary far more, and pension savers in this product segment will experience much higher annual adjustments – in a both negative and positive direction – than savers in the other product segments.

American-Style Indexed Executive Stock Options

This paper develops a new pricing model for American-style indexed executive stock options. We rely on a basic model framework and an indexation scheme first proposed by Johnson and Tian (2000a) in their analysis of European-style indexed options. Our derivation of the valuation formula represents an instructive example of the usefulness of the change-of-numeraire technique. In the papers numerical section we implement the valuation formula and demonstrate that not only may the early exercise premium be significant but also that the delta of the American-style option is typically much larger than the delta of the otherwise identical (value-matched) European-style option. Vega is higher for indexed options than for conventional options but largely independent of whether the options are European- or American-style. This has important implications for the design of executive compensation contracts. We finally extend the analysis to cover the case where the option contracts are subject to delayed vesting. We show that for realistic parameter values, delayed vesting leads only to a moderate reduction in the value of the American-style indexed executive stock option. JEL classifications: G13, G34, J33.

The Bonus-Crediting Mechanism of Danish Pension and Life Insurance Companies: An Empirical Analysis

This paper develops and estimates a model for the bonus-crediting mechanism in relation to with-profits policies issued by Danish life insurance and pension companies. The market for pension and life insurance savings contracts is generally highly opaque, but our proposed model explains a significant part of the variation in actual bonus distribution by Danish market participants. The main determinant of bonus policy is a measure of the degree of solvency which we construct from a unique data set that contains information compiled from several public as well as non-public sources. The data set spans the ten-year period from 1991 to 2000 and the model is estimated by way of maximum likelihood.