Risk Assessment of Life Insurance Contracts : A Comparative Study in a Lévy Framework

Common features in life insurance contracts are an interest rate guarantee andpolicyholder participation in the returns of insurers’ reference portfolio, which canbe of substantial value. The aim of this paper is to analyze the model risk involvedin pricing and risk assessment that arises from the process specification of the referenceportfolio. This is, in general, the most important source of model risk and isanalyzed by comparing results derived in the standard Black-Scholes setting witha Lévy-type model based on a Normal Inverse Gaussian process. We focus onhow the insurer’s insolvency risk associated with fair contracts depends on thespecification of the underlying asset process using lower partial moments. Weshow that even if contracts have the same fair value for the two underlying stochasticasset models, insurers’ shortfall risk can differ tremendously. Model riskcan thus imply substantial solvency risk for insurance companies.