Guarantees in With‐Profit and Unitized With‐Profit Life Insurance Contracts: Fair Valuation Problem in Presence of the Default Option

Abstract

This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractThe purpose of the paper is to apply contingent claim theory to the valuation of the type of participating life insurance policies commonly sold in the UK. The paper extends the techniques developed by Haberman et al. (2003) to allow for the default option. The default option is a feature of the design of these policies, which recognizes that the insurance company's liability is limited by the market value of the reference portfolio of assets underlying the policies that have been sold. The valuation approach is based on the classical contingent claim pricing "machinery", underpinned by Monte Carlo techniques for the computation of fair values. The paper addresses in particular the issue of a fair contract design for a complex type of participating policy and analyzes in detail the feasible set of policy design parameters that would lead to a fair contract and the trade-offs between these parameters.

A general asset–liability management model for the efficient simulation of portfolios of life insurance policies

“…Thereby, a high and thus competitive declaration has to be balanced with a solid financial strength of the company. Various mathematical models for the declaration mechanism are discussed in the literature, see, e.g., [2,6,10,14,15,22,24]. In [14,15,22], the bonus interest rate for the next year is already declared at the beginning of this year (principle of advance declaration) as it is required in some countries, e.g., Germany, by regulation.…”

A Lévy process-based framework for the fair valuation of participating life insurance contracts

“…In fact, since the pioneering work of Brennan and Schwartz (1976) on unit-linked policies, there have been several studies on the different typologies of contract design and their features. Thus we would cite Bacinello (2001Bacinello ( , 2003, Ballotta et al (2004), Jørgensen (2000, 2002), Guillén et al (2004), Haberman et al (2003) and the references therein, and Tanskanen and Lukkarinen (2003), just to mention some of the most recent works.…”

Efficient deterministic numerical simulation of stochastic asset-liability management models in life insurance

“…For a two-dimensional example, this property is illustrated by the grids in Figure 4 where 128 MC points and 128 QMC points are displayed. One can see that the pseudo-random points tend to cluster more and are not as evenly 5 For the fast computation of Φ −1 (x i ), we use Moro's method [29]. 6 The integrand f which results from this transformation is unbounded on the boundary of the unit cube, which is undesirable from a numerical as well as theoretical point of view.…”

“…Much effort has been spent on the development of stochastic asset-liability management (ALM) models for life insurance companies in the last years, see, e.g., [3,4,5,8,13,16,22,27,28] and the references therein. Such models are becoming more and more important due to new accountancy standards, greater globalisation, stronger competition, more volatile capital markets and low interest rates.…”