IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v9y2009i7p803-817.html
   My bibliography  Save this article

Pricing and capital requirements for with profit contracts: modelling considerations

Author

Listed:
  • Laura Ballotta

Abstract

The aim of this paper is to provide an assessment of alternative frameworks for the fair valuation of life insurance contracts with a predominant financial component, in terms of impact on the market consistent price of the contracts, the embedded options, and the capital requirements for the insurer. In particular, we model the dynamics of the log-returns of the reference fund using the so-called Merton (1976) process, which is given by the sum of an arithmetic Brownian motion and a compound Poisson process, and the Variance Gamma (VG) process introduced by Madan and Seneta (1990), and further refined by Madan and Milne (1991) and Madan et al. (1998). We conclude that, although the choice of the market model does not affect significantly the market consistent price of the overall benefit due at maturity, the consequences of a model misspecification on the capital requirements are noticeable.

Suggested Citation

  • Laura Ballotta, 2009. "Pricing and capital requirements for with profit contracts: modelling considerations," Quantitative Finance, Taylor & Francis Journals, vol. 9(7), pages 803-817.
    • Handle: RePEc:taf:quantf:v:9:y:2009:i:7:p:803-817
    DOI: 10.1080/14697680802452068
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/14697680802452068
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/14697680802452068?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Albert N. Shiryaev & Jan Kallsen, 2002. "The cumulant process and Esscher's change of measure," Finance and Stochastics, Springer, vol. 6(4), pages 397-428.
    3. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components1," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 39-55, October.
    4. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components," Working Paper 1159, Economics Department, Queen's University.
    5. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    6. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    7. Friedrich Hubalek & Carlo Sgarra, 2006. "Esscher transforms and the minimal entropy martingale measure for exponential Levy models," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 125-145.
    8. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    9. Grosen, Anders & Løchte Jørgensen, Peter, 2001. "Life Insurance Liabilities at Market Value," Finance Working Papers 01-4, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    10. Laura Ballotta & Steven Haberman & Nan Wang, 2006. "Guarantees in With‐Profit and Unitized With‐Profit Life Insurance Contracts: Fair Valuation Problem in Presence of the Default Option," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(1), pages 97-121, March.
    11. 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.
    12. Bacinello, Anna Rita, 2001. "Fair Pricing of Life Insurance Participating Policies with a Minimum Interest Rate Guaranteed," ASTIN Bulletin, Cambridge University Press, vol. 31(2), pages 275-297, November.
    13. Ballotta, Laura, 2005. "A Lévy process-based framework for the fair valuation of participating life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 173-196, October.
    14. Grosen, Anders & Lochte Jorgensen, Peter, 2000. "Fair valuation of life insurance liabilities: The impact of interest rate guarantees, surrender options, and bonus policies," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 37-57, February.
    15. 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.
    16. 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.
    17. Kassberger, Stefan & Kiesel, Rüdiger & Liebmann, Thomas, 2008. "Fair valuation of insurance contracts under Lévy process specifications," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 419-433, February.
    18. Ballotta, Laura & Esposito, Giorgia & Haberman, Steven, 2006. "The IASB Insurance Project for life insurance contracts: Impact on reserving methods and solvency requirements," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 356-375, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ballotta, Laura & Eberlein, Ernst & Schmidt, Thorsten & Zeineddine, Raghid, 2021. "Fourier based methods for the management of complex life insurance products," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 320-341.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ballotta, Laura, 2005. "A Lévy process-based framework for the fair valuation of participating life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 173-196, October.
    2. Liuren Wu, 2006. "Dampened Power Law: Reconciling the Tail Behavior of Financial Security Returns," The Journal of Business, University of Chicago Press, vol. 79(3), pages 1445-1474, May.
    3. Winston Buckley & Sandun Perera, 2019. "Optimal demand in a mispriced asymmetric Carr–Geman–Madan–Yor (CGMY) economy," Annals of Finance, Springer, vol. 15(3), pages 337-368, September.
    4. Kao, Lie-Jane & Wu, Po-Cheng & Lee, Cheng-Few, 2012. "Time-changed GARCH versus the GARJI model for prediction of extreme news events: An empirical study," International Review of Economics & Finance, Elsevier, vol. 21(1), pages 115-129.
    5. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    6. Chan, Tat Lung (Ron), 2019. "Efficient computation of european option prices and their sensitivities with the complex fourier series method," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    7. Olivier Le Courtois & François Quittard-Pinon & Xiaoshan Su, 2020. "Pricing and hedging defaultable participating contracts with regime switching and jump risk," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 303-339, June.
    8. Jingzhi Huang & Liuren Wu, 2004. "Specification Analysis of Option Pricing Models Based on Time- Changed Levy Processes," Finance 0401002, University Library of Munich, Germany.
    9. George Bouzianis & Lane P. Hughston, 2019. "Determination Of The Lévy Exponent In Asset Pricing Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(01), pages 1-18, February.
    10. Athanassios N. Avramidis & Pierre L'Ecuyer, 2006. "Efficient Monte Carlo and Quasi-Monte Carlo Option Pricing Under the Variance Gamma Model," Management Science, INFORMS, vol. 52(12), pages 1930-1944, December.
    11. Ballotta, Laura & Esposito, Giorgia & Haberman, Steven, 2006. "The IASB Insurance Project for life insurance contracts: Impact on reserving methods and solvency requirements," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 356-375, December.
    12. Abdou Kélani & François Quittard-Pinon, 2017. "Pricing and Hedging Variable Annuities in a Lévy Market: A Risk Management Perspective," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(1), pages 209-238, March.
    13. Svetlana Boyarchenko & Sergei Levendorskiĭ, 2019. "Sinh-Acceleration: Efficient Evaluation Of Probability Distributions, Option Pricing, And Monte Carlo Simulations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-49, May.
    14. Bernard, Carole & Boyle, Phelim P., 2011. "A Natural Hedge for Equity Indexed Annuities," Annals of Actuarial Science, Cambridge University Press, vol. 5(2), pages 211-230, September.
    15. Yacine Aït-Sahalia & Jean Jacod, 2012. "Analyzing the Spectrum of Asset Returns: Jump and Volatility Components in High Frequency Data," Journal of Economic Literature, American Economic Association, vol. 50(4), pages 1007-1050, December.
    16. repec:dau:papers:123456789/1392 is not listed on IDEAS
    17. Vladimir K. Kaishev & Dimitrina S. Dimitrova, 2009. "Dirichlet Bridge Sampling for the Variance Gamma Process: Pricing Path-Dependent Options," Management Science, INFORMS, vol. 55(3), pages 483-496, March.
    18. Olivier Le Courtois & François Quittard-Pinon, 2008. "Fair Valuation of Participating Life Insurance Contracts with Jump Risk," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 33(2), pages 106-136, December.
    19. Khaled Salhi, 2017. "Pricing European options and risk measurement under exponential Lévy models — a practical guide," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-36, June.
    20. Jacques Pézier & Johanna Scheller, 2011. "A Comprehensive Evaluation of Portfolio Insurance Strategies," ICMA Centre Discussion Papers in Finance icma-dp2011-15, Henley Business School, University of Reading.
    21. Tat Lung Chan, 2017. "Singular Fourier-Pad\'e Series Expansion of European Option Prices," Papers 1706.06709, arXiv.org, revised Nov 2017.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:quantf:v:9:y:2009:i:7:p:803-817. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.