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 participating (or with profits) policy. This type of contract stand in contrast to Unit-Linked (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 ULL products, the participating policies are typically equipped with an interest rate guarantee and possibly also an option to surrender (sell-back) the policy to the LAC 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 LAC solvency can be quickly jeopardised if earning opportunities deteriorate in a situation where bonus reserves are low and promised returns are high.

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.

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

The article 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 that 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, whereas the more complex ones are analysed using numerical (finite difference) procedures. We accompany our theoretical results with illustrative numerical examples as we proceed.Ship valuation, options on ships, leasing, lease contracts with options, optimal stopping,

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. The Geneva Papers on Risk and Insurance Theory (2001) 26, 57–84. doi:10.1023/A:1011264408187