Fair Valuation of Participating Life Insurance Contracts with Jump Risk

Abstract

The purpose of this article is to value participating life insurance contracts when the linked portfolio is modeled by a jump-diffusion. More precisely, this process has a Brownian component and a compound Poisson one, where the jump size is driven by a double exponential distribution. Specifically here, the bankruptcy risk of the insurance company is considered. Thus, market and credit risks are taken into account. A quasi-closed-form formula is obtained in fair value for the price of the considered life insurance contract. This allows us to investigate the impact of strategic parameters as well as structural ones, as is shown in the numerical section of this paper. In particular, we study the impact on the contract of the volatility, jump intensity, jump asymmetry, company leverage, guaranteed rate, participation rate and level of the default barrier, and comment on how they are likely to increase the probability of early default of the issuer.

Is Fair Pricing Possible? An Analysis of Participating Life Insurance Portfolios

“…In general, researchers have focused on finding a suitable set of design parameters that could lead to a fair valuation of such contracts. Many studies have also investigated the interactions between the contract parameters that define the insurer's and customers’ risk situations, (e.g., Gatzert and Kling, ; Kling, Richter, and Ruß, , Le Courtois and Quittard‐Pinon(; Schmeiser and Wagner, ). Other authors, such as, Kling et al.…”

“…In general, researchers have focused on finding a suitable set of design parameters that could lead to a fair valuation of such contracts. Many studies have also investigated the interactions between the contract parameters that define the insurer's and customers' risk situations (e.g., Gatzert and Kling, 2007;Kling, Richter, and Ruß, 2007b;Le Courtois and Quittard-Pinon, 2008;Schmeiser and Wagner, 2015). Other authors, such as Ruß (2007a,2007b), Graf, Richter, and Ruß (2011), Zemp (2011), and Bohnert and Gatzert (2012), have investigated different schemes for distributing surplus and the effects of such schemes on both the fair valuation of contracts and the insurer's risk exposure.…”

Impacts of Jumps and Stochastic Interest Rates on the Fair Costs of Guaranteed Minimum Death Benefit Contracts

“…Ballotta (2005) was the first author to analyze the impacts of jumps in valuing participating life insurance contracts, using a jump diffusion process with Gaussian jumps while Kassberger, Kiesel, and Liebmann (2007) made use of Meixner and NIG processes. Le Courtois and Quittard-Pinon (2008) used a Kou process and took into account early default in with-profits life insurance contracts. In this article, we also consider a Kou process, a jump diffusion process whose jumps have a double exponential distribution (see Kou (2002).…”

Valuation of Equity-Linked Life Insurance Contracts with Flexible Guarantees in a Non Gaussian Economy

“…However now it is well recognized that financial asset returns generally cannot be represented by normal laws, because of empirical leptokurtic distribution. Non-normal and in particular Lévy processes have recently been introduced by Kassberger, Kiesel, and Liebmann (2007), and by Le Courtois and Quittard-Pinon (2008).…”