RISK ANALYSIS OF ANNUITY CONVERSION OPTIONS IN A STOCHASTIC MORTALITY ENVIRONMENT

• Published in: ASTIN Bulletin : The Journal of the IAA Vol. 44; no. 2; pp. 197 - 236
• Main Authors: Kling, Alexander, Ruß, Jochen, Schilling, Katja
• Format: Journal Article
• Language: English; French
• Published: New York, USA Cambridge University Press 01.05.2014
• Subjects: Actuarial science; guaranteed minimum income benefit; longevity risk; guaranteed annuity option; valuation and risk analysis of embedded guarantees; Financial risk
• ISSN: 0515-0361; 1783-1350
• DOI: 10.1017/asb.2014.7

While extensive literature exists on the valuation and risk management of financial guarantees embedded in insurance contracts, both the corresponding longevity guarantees and interactions between financial and longevity guarantees are often ignored. The present paper provides a framework for a joint analysis of financial and longevity guarantees, and applies this framework to different annuity conversion options in deferred unit-linked annuities. In particular, we analyze and compare different versions of so-called guaranteed annuity options and guaranteed minimum income benefits with respect to the value of the option and the resulting risk for the insurer. Furthermore, we examine whether and to what extent an insurance company is able to reduce the risk by typical risk management strategies. The analysis is based on a combined stochastic model for both financial market and future survival probabilities. We show that different annuity conversion options have significantly different option values, and that different risk management strategies lead to a significantly different risk for the insurance company.