Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-06-08T00:40:03.715Z Has data issue: false hasContentIssue false
  • English
  • Français

Evaluation of equity-linked products in the presence of policyholder surrender option using risk-control strategies

Published online by Cambridge University Press:  08 March 2021

Patrice Gaillardetz ,
Saeb Hachem  and
Mehran Moghtadai
Patrice Gaillardetz*
Affiliation:
Department of Mathematics, Statistics at Concordia University, Montreal, Canada
Mehran Moghtadai
Affiliation:
Innovation Department at TD Insurance, Montreal, Canada
*
*Corresponding author. E-mail: patrice.gaillardetz@concordia.ca
Get access Rights & Permissions [Opens in a new window]

Abstract

Throughout the past couple of decades, the surge in the sale of equity-linked products has led to many discussions on the evaluation and risk management of surrender options embedded in these products. However, most studies treat such options as American/Bermudian style options. In this article, a different approach is presented where only a portion of the policyholders react optimally due to the belief that not all policyholders are rational. Through this method, a probability of surrender is obtained based on the option moneyness and the product is partially hedged using local risk-control strategies. This partial hedging approach is versatile since few assumptions are required for the financial framework. To compare the different surrender assumptions, the initial capital requirement for an equity-linked product is obtained under a regime-switching equity model. Numerical examples illustrate the dynamics and efficiency of this hedging approach.

Keywords

Equity-linked productsRisk managementPartial hedgingLocal risk minimizing strategySurrender riskRegime switching equity model
Type
Original Research Paper
Information
Annals of Actuarial Science , Volume 16 , Issue 1 , March 2022 , pp. 25 - 41
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Institute and Faculty of Actuaries

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Artzner, P., Delbaen, F., Eber, J.-M. & Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9(3), 203–228.CrossRefGoogle Scholar
Bacinello, A.R. (2004). Modelling the surrender conditions in equity-linked life insurance. Quaderni del Dipartimento di Matematica Applicata alle Scienze Economiche Statistiche e Attuariali” Bruno de Finetti”, Università degli Studi di Trieste, 2.Google Scholar
Barber, B.M. & Odean, T. (2011). The behavior of individual investors. Handbook of the Economics of Finance, 2, 1533–1570.CrossRefGoogle Scholar
Bauer, D., Kling, A. & Russ, J. (2008) A universal pricing framework for guaranteed minimum benefits in variable annuities. ASTIN Bulletin, 38(2), 621.CrossRefGoogle Scholar
Bollen, N.P.B. (1998). Valuing options in regime-switching models. The Journal of Derivatives, 6(1), 38–49.CrossRefGoogle Scholar
Bowers, N.L. (1997). Actuarial Mathematics. Society of Actuaries. ISBN 9780938959465.Google Scholar
Coleman, T.F., Li, Y. & Patron, M.C. (2006). Hedging guarantees in variable annuities under both equity and interest rate risks. Insurance: Mathematics and Economics, 38(2), 215–228.Google Scholar
De Giovanni, D. (2010). Lapse rate modeling: a rational expectation approach. Scandinavian Actuarial Journal, 2010(1), 56–67.CrossRefGoogle Scholar
Föllmer, H. & Schweizer, M. (1988). Hedging by sequential regression: an in- troduction to the mathematics of option trading. Astin Bulletin, 2, 147–160.CrossRefGoogle Scholar
Föllmer, H. & Sondermann, D. (1986). Hedging of non-redundant contingent claims. Contributions to Mathematical Economics, 205–223.Google Scholar
Forsyth, P.A. & Vetzal, K. (2014). An optimal stochastic control framework for determining the cost of hedging of variable annuities. Journal of Economic Dynamics and Control, 44, 29–53.CrossRefGoogle Scholar
Gaillardetz, P. & Hachem, S. (2019). Control-risk strategies. arXiv .Google Scholar
Gaillardetz, P. & Moghtadai, M. (2017). Partial hedging for equity-linked products using risk-minimising strategies. North American Actuarial Journal, 21(4), 580–59.CrossRefGoogle Scholar
Gerber, H.U. & Shiu, E.S.W. (1994). Option pricing by esscher transforms. Transactions of the Society of Actuaries, 46, 99–140.Google Scholar
Grosen, A. & Jørgensen, P.L. (1997). Valuation of early exercisable interest rate guarantees. Journal of Risk and Insurance, 64(3), 481–503.CrossRefGoogle Scholar
Grosen, A. & Jørgensen, P.L. (2000). Fair valuation of life insurance liabilities: the impact of interest rate guarantees, surrender options, and bonus policies. Insurance: Mathematics and Economics, 26(1), 37–57.Google Scholar
Hamilton, J.D. (1989). A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica: Journal of the Econometric Society, 57, 357–384.CrossRefGoogle Scholar
Hardy, M. (2003). Investment Guarantees: Modeling and Risk Management for Equity-Linked Life Insurance. Hoboken, NJ: John Wiley & Sons.Google Scholar
IRI. (2019). Iri issues 2018 fourth quarter annuity sales report. Available online at the address https://www.irionline.org.Google Scholar
Kling, A., Ruez, F. & Ruß, J. (2014). The impact of policyholder behavior on pricing, hedging, and hedge efficiency of withdrawal benefit guarantees in variable annuities. European Actuarial Journal, 4(2), 281–314.CrossRefGoogle Scholar
Kuo, W., Tsai, C. & Chen, W.-K. (2003). An empirical study on the lapse rate: the cointegration approach. Journal of Risk and Insurance, 70(3), 489–508.CrossRefGoogle Scholar
Moghtadai, M. (2014). Partial Hedging of Equity Linked Products in the Presence of Policyholder Surrender Using Risk Measures (master’s thesis). Master’s thesis, Concordia University.Google Scholar
Moller, T. (1998). Risk-minimising hedging strategies for unit linked life insurance contratcs. ASTIN Bulletin, 28, 17–47.CrossRefGoogle Scholar
Rockafellar, R.T. & Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of Risk, 2, 21–41.CrossRefGoogle Scholar
Schweizer, M. (1988). Hedging of Options in a General Semimartingale Model. PhD thesis, ETH Zurich.Google Scholar