On the Risk-Neutral Valuation of Life Insurance Contracts with Numerical Methods in View

Abstract

In recent years, market-consistent valuation approaches have gained an increasing importance for insurance companies. This has triggered an increasing interest among practitioners and academics, and a number of specifi c studies on such valuation approaches have been published.In this paper, we present a generic model for the valuation of life insurance contracts and embedded options. Furthermore, we describe various numerical valuation approaches within our generic setup. We particularly focus on contracts containing early exercise features since these present (numerically) challenging valuation problems.Based on an example of participating life insurance contracts, we illustrate the different approaches and compare their effi ciency in a simple and a generalized Black-Scholes setup, respectively. Moreover, we study the impact of the considered early exercise feature on our example contract and analyze the infl uence of model risk by additionally introducing an exponential Lévy model.

Policyholder Exercise Behavior in Life Insurance: The State of Affairs

“…The finding that value is the most important driver of policyholder behavior in variable products is broadly in line with the general approach in the actuarial literature, where these problems are commonly solved using value-maximizing approaches akin to the valuation of American or Bermudan option (see Bauer et al (2010) and references therein). However, as already indicated, several studies have found discrepancies with corresponding results and market observations when following the value-maximizing approach.…”

“…This is not to say that actually determining the optimal strategies within a risk-neutral valuation framework is trivial. It may require the solution of optimal control problems akin to the valuation of American or Bermudan options, and a great number of contributions in actuarial science have taken this approach to evaluate various types of contracts (Milevsky and Salisbury, 2006;Ulm, 2006;Bauer et al, 2008;Dai et al, 2008;Bauer et al, 2010;Bacinello et al, 2011, among many others).…”

“…However, before heading down this path, it is worth pointing out that although a basic value-maximizing approach may fail at aligning theory with observations, this approach can be important for risk management. More precisely, the approach identifies the worst-case scenario from the insurer's point of view that is robust to any exercise strategy, even lucky or prescient ones (Bauer et al, 2010. Thus, one way to account for the risk associated with policyholder behavior is to (i) determine the value associated with value-maximizing behavior and put up the difference to the market price as a policyholder behavior risk reserve; and (ii) manage embedded risk as if policyholders behaved as value maximizers.…”

Improving Optimal Terminal Value Replicating Portfolios

“…This setup roughly follows that of [3]: Let Ω, F , (F t ) t∈T , Q be a filtered probability space 1 in discrete time T := {t = 0, 1 . .…”

“…In the last years, market consistent valuation has become the standard approach toward risk management of life insurance policies, see for example [3]. Due to the complexity of life insurance contracts, most academics and practitioners resort to Monte Carlo methods for valuation purposes.…”