Anders Grosen

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.

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.