Variable Annuities in a Lévy-Based Hybrid Model With Surrender Risk

41 Pages Posted: 10 Jun 2019

See all articles by Laura Ballotta

Laura Ballotta

Sir John Cass Business School - City, University of London

Ernst Eberlein

University of Freiburg

Thorsten Schmidt

University of Freiburg

Raghid Zeineddine

affiliation not provided to SSRN

Date Written: May 23, 2019

Abstract

This paper proposes a market consistent valuation framework for variable annuities 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 price of the variable annuity 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

Suggested Citation

Ballotta, Laura and Eberlein, Ernst and Schmidt, Thorsten and Zeineddine, Raghid, Variable Annuities in a Lévy-Based Hybrid Model With Surrender Risk (May 23, 2019). Available at SSRN: https://ssrn.com/abstract=3392939 or http://dx.doi.org/10.2139/ssrn.3392939

Laura Ballotta (Contact Author)

Sir John Cass Business School - City, University of London ( email )

Faculty of Finance
106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

HOME PAGE: http://www.city.ac.uk/people/academics/laura-ballotta

Ernst Eberlein

University of Freiburg ( email )

Department of Mathematical Stochastics
Eckerstrasse 1
D-79104, Freiburg
Germany
++49 761 203 5660 (Phone)
++49 761 203 5661 (Fax)

Thorsten Schmidt

University of Freiburg ( email )

Fahnenbergplatz
Freiburg, D-79085
Germany

Raghid Zeineddine

affiliation not provided to SSRN

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