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Evaluating fair premiums of equity-linked policies with surrender option in a bivariate model

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  • Costabile, Massimo
  • Gaudenzi, Marcellino
  • Massabò, Ivar
  • Zanette, Antonino

Abstract

We tackle the problem of computing fair periodical premiums of an equity-linked policy with a maturity guarantee and an embedded surrender option. We consider the policy as a Bermudan-style contingent claim that can be exercised at the premium payment dates. The evaluation framework is based on a discretization of a bivariate model that considers the joint evolution of the equity value with stochastic interest rates. To deeply reduce the computational complexity of the pricing problem we use the singular points framework that allows us to compute accurate upper and lower estimates of the policy premiums.

Suggested Citation

  • Costabile, Massimo & Gaudenzi, Marcellino & Massabò, Ivar & Zanette, Antonino, 2009. "Evaluating fair premiums of equity-linked policies with surrender option in a bivariate model," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 286-295, October.
    • Handle: RePEc:eee:insuma:v:45:y:2009:i:2:p:286-295
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    References listed on IDEAS

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    1. Costabile, Massimo & Massabó, Ivar & Russo, Emilio, 2008. "A binomial model for valuing equity-linked policies embedding surrender options," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 873-886, June.
    2. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    3. Aase Nielsen, J. & Sandmann, Klaus, 1995. "Equity-linked life insurance: A model with stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 16(3), pages 225-253, July.
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    5. Bacinello, Anna Rita, 2005. "Endogenous model of surrender conditions in equity-linked life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 270-296, October.
    6. 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.
    7. 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.
    8. 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.
    9. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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    Cited by:

    1. Nielsen, J. Aase & Sandmann, Klaus & Schlögl, Erik, 2011. "Equity-linked pension schemes with guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 547-564.
    2. Hürlimann, Werner, 2010. "Analytical Pricing of the Unit-Linked Endowment with Guarantees and Periodic Premiums," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 631-653, November.
    3. Thomas Poufinas, 2015. "On the pricing of regular premium variable annuities using options," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 4(1), pages 54-77.
    4. Gan, Guojun, 2013. "Application of data clustering and machine learning in variable annuity valuation," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 795-801.
    5. Giulia De Rossi & Tiziano Vargiolu, 2010. "Optimal prepayment and default rules for mortgage-backed securities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 33(1), pages 23-47, May.

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