IDEAS home Printed from https://ideas.repec.org/a/sbe/breart/v27y2007i2a1529.html
   My bibliography  Save this article

A General Approach for Pricing Rollover Options

Author

Listed:
  • Zimmer, Christian Johannes

Abstract

When an insurance company sells a mutual fund with death and maturity guarantees to its client, it may consider allowing the client to extend the guarantee for some more years. If the renewal only happens once, a so-called rollover option is implied in the contract. In this paper, we show how the generalized Bermudan option can be applied to the special case of the rollover option. By avoiding the heavy mathematical tools which are necessary to prove the existence of a hedging strategy, we will focus on the calculations that are common in the Black-Scholestype analysis. Contrary to Bilodeau (1997) who analyzed the one-time renewal, we can refer to the results on the (generalized) Bermudan option for which the existence of a hedging strategy was already proved. We will see that the strike price has to be adjusted if the contract is renewed in order to explicitly calculate the price of the contract.

Suggested Citation

  • Zimmer, Christian Johannes, 2007. "A General Approach for Pricing Rollover Options," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 27(2), November.
    • Handle: RePEc:sbe:breart:v:27:y:2007:i:2:a:1529
    as

    Download full text from publisher

    File URL: https://periodicos.fgv.br/bre/article/view/1529
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bilodeau, Claire, 1997. "Better late than never: The case of the rollover option," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 103-111, November.
    2. Peter Carr & Robert Jarrow & Ravi Myneni, 2008. "Alternative Characterizations Of American Put Options," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 5, pages 85-103, World Scientific Publishing Co. Pte. Ltd..
    Full references (including those not matched with items on IDEAS)

    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. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, January.
    2. Jérôme Detemple, 1999. "American Options: Symmetry Properties," CIRANO Working Papers 99s-45, CIRANO.
    3. João Nunes, 2011. "American options and callable bonds under stochastic interest rates and endogenous bankruptcy," Review of Derivatives Research, Springer, vol. 14(3), pages 283-332, October.
    4. D. J. Manuge, 2013. "Multi-Asset Option Pricing with Exponential L\'evy Processes and the Mellin Transform," Papers 1309.3035, arXiv.org.
    5. Masaaki Fujii & Seisho Sato & Akihiko Takahashi, 2012. "An FBSDE Approach to American Option Pricing with an Interacting Particle Method," CARF F-Series CARF-F-302, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    6. Ibáñez, Alfredo, 2008. "Factorization of European and American option prices under complete and incomplete markets," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 311-325, February.
    7. Damien Lamberton & Mohammed Mikou, 2013. "Exercise boundary of the American put near maturity in an exponential Lévy model," Finance and Stochastics, Springer, vol. 17(2), pages 355-394, April.
    8. Cheng Cai & Tiziano De Angelis & Jan Palczewski, 2021. "The American put with finite-time maturity and stochastic interest rate," Papers 2104.08502, arXiv.org, revised Feb 2024.
    9. Jérôme Detemple, 2014. "Optimal Exercise for Derivative Securities," Annual Review of Financial Economics, Annual Reviews, vol. 6(1), pages 459-487, December.
    10. Battauz, A. & Pratelli, M., 2004. "Optimal stopping and American options with discrete dividends and exogenous risk," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 255-265, October.
    11. Cosma, Antonio & Galluccio, Stefano & Pederzoli, Paola & Scaillet, Olivier, 2020. "Early Exercise Decision in American Options with Dividends, Stochastic Volatility, and Jumps," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(1), pages 331-356, February.
    12. Feng Dai & Feng Han, 2004. "Optimal Choice Models for Executing Time to American Options," Finance 0412016, University Library of Munich, Germany.
    13. Shiller, Robert J. & Wojakowski, Rafal M. & Ebrahim, M. Shahid & Shackleton, Mark B., 2019. "Continuous Workout Mortgages: Efficient pricing and systemic implications," Journal of Economic Behavior & Organization, Elsevier, vol. 157(C), pages 244-274.
    14. Antonio Cosma & Stefano Galluccio & Paola Pederzoli & O. Scaillet, 2012. "Valuing American Options Using Fast Recursive Projections," Swiss Finance Institute Research Paper Series 12-26, Swiss Finance Institute.
    15. Weiping Li & Su Chen, 2018. "The Early Exercise Premium In American Options By Using Nonparametric Regressions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(07), pages 1-29, November.
    16. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2009. "Computation in an Asymptotic Expansion Method," CARF F-Series CARF-F-149, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    17. Asbjørn T. Hansen & Peter Løchte Jørgensen, 2000. "Analytical Valuation of American-Style Asian Options," Management Science, INFORMS, vol. 46(8), pages 1116-1136, August.
    18. Luca Vincenzo Ballestra, 2018. "Fast and accurate calculation of American option prices," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 399-426, November.
    19. Fabozzi, Frank J. & Paletta, Tommaso & Stanescu, Silvia & Tunaru, Radu, 2016. "An improved method for pricing and hedging long dated American options," European Journal of Operational Research, Elsevier, vol. 254(2), pages 656-666.
    20. Elizondo Rocío & Padilla Pablo & Bladt Mogens, 2009. "An Alternative Formula to Price American Options," Working Papers 2009-06, Banco de México.

    More about this item

    Statistics

    Access and download statistics

    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:sbe:breart:v:27:y:2007:i:2:a:1529. 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: Núcleo de Computação da FGV EPGE (email available below). General contact details of provider: https://edirc.repec.org/data/sbeeeea.html .

    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.