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How sensitive is the pricing of lookback and interest rate guarantees when changing the modelling assumptions?

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  • Orozco-Garcia, Carolina
  • Schmeiser, Hato

Abstract

This paper aims to give detailed insights into the price sensitivity of embedded investment guarantees provided by unit-linked life insurance products. Particularly, it analyzes the model and parameter risk from the provider’s perspective. We compare two different forms of investment guarantees: Interest Rate Guarantees (IRG) and Lookback Guarantees (LBG). Via Monte Carlo simulation, the prices of the embedded investment guarantees are estimated assuming the underlying to evolve according to a normal or double-exponential jump–diffusion model. The input parameters are derived from empirical data for various asset classes. In a first step, the parameters of the IRG and the LBG are adjusted such the prices of these two guarantees are equal. In a second step, a detailed comparison is made between the price sensitivities of both guarantee forms when the initial modelling parameters are changed. Finally, we investigate how parameter changes affect the investor payoff under the different guarantee forms and model assumptions used for the dynamic of the underlying.

Suggested Citation

  • Orozco-Garcia, Carolina & Schmeiser, Hato, 2015. "How sensitive is the pricing of lookback and interest rate guarantees when changing the modelling assumptions?," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 77-93.
    • Handle: RePEc:eee:insuma:v:65:y:2015:i:c:p:77-93
    DOI: 10.1016/j.insmatheco.2015.08.004
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    References listed on IDEAS

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    1. Conze, Antoine & Viswanathan, 1991. "Path Dependent Options: The Case of Lookback Options," Journal of Finance, American Finance Association, vol. 46(5), pages 1893-1907, December.
    2. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    3. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    4. McLachlan, Geoffrey J. & Krishnan, Thriyambakam & Ng, See Ket, 2004. "The EM Algorithm," Papers 2004,24, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    5. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
    6. Nadine Gatzert & Carin Huber & Hato Schmeiser, 2011. "On the Valuation of Investment Guarantees in Unit-linked Life Insurance: A Customer Perspective," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 36(1), pages 3-29, January.
    7. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    8. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    9. Hans Gerber & Elias Shiu, 2003. "Pricing Lookback Options and Dynamic Guarantees," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(1), pages 48-66.
    10. Bacinello, Anna Rita & Ortu, Fulvio, 1993. "Pricing equity-linked life insurance with endogenous minimum guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 12(3), pages 245-257, June.
    11. Lee, Hangsuck, 2003. "Pricing equity-indexed annuities with path-dependent options," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 677-690, December.
    12. Brennan, Michael J. & Schwartz, Eduardo S., 1976. "The pricing of equity-linked life insurance policies with an asset value guarantee," Journal of Financial Economics, Elsevier, vol. 3(3), pages 195-213, June.
    13. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    14. Cyrus Ramezani & Yong Zeng, 2007. "Maximum likelihood estimation of the double exponential jump-diffusion process," Annals of Finance, Springer, vol. 3(4), pages 487-507, October.
    15. Bacinello, Anna Rita & Ortu, Fulvio, 1993. "Pricing equity-linked life insurance with endogenous minimum guarantees : A corrigendum," Insurance: Mathematics and Economics, Elsevier, vol. 13(3), pages 303-304, December.
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    Cited by:

    1. Daliana Luca & Hato Schmeiser & Florian Schreiber, 2023. "Investment guarantees in financial products: an analysis of consumer preferences," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 48(4), pages 906-940, October.

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