Variable annuities in a Lévy-based hybrid model with surrender risk

Abstract

This paper proposes a market consistent valuation framework for variable annuities (VAs) with guaranteed minimum accumulation benefit, death benefit and surrender benefit features. The setup is based on a hybrid model for the financial market and uses time-inhomogeneous Lévy processes as risk drivers. Further, we allow for dependence between financial and surrender risks. Our model leads to explicit analytical formulas for the quantities of interest, and practical and efficient numerical procedures for the evaluation of these formulas. We illustrate the tractability of this approach by means of a detailed sensitivity analysis of the fair value of the VA and its components with respect to the model parameters. The results highlight the role played by the surrender behaviour and the importance of its appropriate modelling.

Keywords:

• Finance
• Variable annuities
• Hybrid models
• Lévy processes
• Surrender risk

JEL Classification:

• G13
• G12
• G22
• C63

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Laura Ballotta http://orcid.org/0000-0002-2059-6281

Ernst Eberlein http://orcid.org/0000-0001-8935-2341

Thorsten Schmidt http://orcid.org/0000-0001-9254-4010

Supplemental data

Supplemental data for this article can be accessed at: http://dx.doi.org/10.1080/14697688.2019.1687929.

Notes

† ‘Lapse’ was originally used to denote termination of an insurance policy and loss of coverage because the policyholder had failed to pay premia, whilst ‘surrender’ denotes termination accompanied by the payout of a surrender benefit. Nowadays ‘lapse’ often denotes both situations.

Additional information

Funding

The authors gratefully acknowledge the financial support from the Freiburg Institute for Advanced Studies (FRIAS) within the FRIAS Research Project ‘Linking Finance and Insurance: Theory and Applications (2017–2019)’.