IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

A discrete martingale model of pension fund guarantees in

Listed author(s):
  • Klaus P. Fischer

    (Laval University)

In this paper we present a solution to the problem of pricing guarantees of minimum returns on pension fund contributions. These guarantees exist by law in Colombia and cover all pension fund contributions made to the country's private pension fund administration companies (AFPs). As of September 1997, the funds were collecting contributions of 2.5 million affiliates with an accumulated capital of 1.8 billion dollars starting from zero in 1994. Two types of guarantees exist: on obligatory contributions and on voluntary contributions. The solutions are based on a discrete martingale approach . We show that both guarantees are equivalent to an ''option to exchange.'' However, in the case of voluntary contributions a ceiling on the payoff s must be added. Using a discrete martingale framework and a binomial solution we develop all aspects of the model that are necessary for its practical application in the context of the pension fund guarantees. Binomial formulas are obtained for both forms of guarantees. Besides solving the problem of pricing the guarantees offered by insurance fund, the contributions in terms of options theory of this paper are: i) we adapt the binomila model of options to exchange to relate the relevant parameters of the same to a continuous-time lognormal process; ii) we provide a binomial solution to the problem of an option to exchange with a ceiling. We then investigate the incentives that the current fixed-price system introduces and propose possible systems of incentives that can be used to encourage higher-risk investment by the AFP's and a shift of the fund's portfolio to risky equity and debt. Given the country's effort to encourage capital markets development and the financing of the real sector via private financial markets, this strategy appears to be desirable from the social and economic point of view.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: no

Paper provided by EconWPA in its series Finance with number 9802003.

in new window

Length: 30 pages
Date of creation: 19 Feb 1998
Handle: RePEc:wpa:wuwpfi:9802003
Note: Type of Document - PDF; prepared on IBM PC; to print on HP/PostScript; pages: 30 ; figures: included
Contact details of provider: Web page:

No references listed on IDEAS
You can help add them by filling out this form.

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpfi:9802003. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.