IDEAS home Printed from
   My bibliography  Save this paper

"Valuing Variable Annuities" (in Japanese)


  • Takao Kobayashi

    (Faculty of Economics, University of Tokyo)

  • Ryoichi Ikeda

    (Graduate School of Economics, University of Tokyo)

  • Yoichiro Hasegawa

    (Rating and Investment Information, Inc.)


In this paper we propose a framework to evaluate variable annuities. We show that the invested capital to a variable annuity can be decomposed into: (i) the reserve money in the account, (ii) options, (iii) fees paid to the mutual fund companies, and (iv) margin accruing to the insurance company. The first two components comprise value to the insured, and the last two accrue to the supply side companies. This view provides a convenient method to double-check the computation of various components of value. We also show that death benefit option attached to the most popular variable annuities is a portfolio of European put options of differing maturities. Assuming that investment value follows a geometric Brownian motion, this component can be valued applying the Black-Scholes formula and using the "death rates statistics" published by the Ministry of Heath, Labour and Welfare. Options on the income benefit are also valued using the Black-Scholes formula. @Stepped-up death benefit is a form of look-back options, which we value using a trinomial lattice. We value some typical products assuming that a person purchases them at age 40 and at age 50. We then examine how various value components would change in response to the volatilities of the investment products, the length of the contract and so on.

Suggested Citation

  • Takao Kobayashi & Ryoichi Ikeda & Yoichiro Hasegawa, 2003. ""Valuing Variable Annuities" (in Japanese)," CIRJE J-Series CIRJE-J-92, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:jseres:2003cj92

    Download full text from publisher

    File URL:
    Download Restriction: no

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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:tky:jseres:2003cj92. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: CIRJE administrative office (email available below). General contact details of provider: .

    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.