IDEAS home Printed from
MyIDEAS: Login to save this paper or follow this series

From Measure Changes to Time Changes in Asset Pricing

  • Geman, Hélyette
Registered author(s):

    The goal of the paper is to review the last 35 years of continuous-time finance by focusing on two major advances: (i) The powerful elegance of the martingale representation for primitive assets and attainable contingent claims in more and more general settings, thanks to the probabilistic tool of probability change and the economic flexibility in the choice of the numéraire relative to which prices are expressed. This numéraire evolved over time from the money market account to a zero-coupon bond or a stock price, lastly to strictly positive quantities involved in the Libor or swap market models and making the pricing of caps or swaptions quite efficient. (ii) The persistent central role of Brownian motion in finance across the 20th century: even when the underlying asset price is a very general semi-martingale, the no-arbitrage assumption and Monroe theorem [Monroe, I., 1978. Processes that can be embedded in Brownian motion. Annals of Probability 6, 42–56] allow us to write it as Brownian motion as long as we are willing to change the time. The appropriate stochastic clock can be shown empirically to be driven by the cumulative number of trades, hence by market activity. Consequently, starting with a general multidimensional stochastic process S defined on a probability space (Ω, , P) and representing the prices of primitive securities, the no-arbitrage assumption allows, for any chosen numéraire, to obtain a martingale representation for S under a probability measure QS equivalent to P. This route will be particularly beneficiary for the pricing of complex contingent claims. Alternatively, changing the clock, i.e., changing the filtration (), we can recover the Brownian motion and normality of returns. In all cases martingales appear as the central representation of asset prices, either through a measure change or through a time change.

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below under "Related research" whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Paper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/1388.

    in new window

    Date of creation: May 2005
    Date of revision:
    Publication status: Published in Journal of Banking and Finance, 2005, Vol. 29, no. 11. pp. 2701-2722.Length: 21 pages
    Handle: RePEc:dau:papers:123456789/1388
    Contact details of provider: Web page:

    More information through EDIRC

    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:dau:papers:123456789/1388. 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: (Alexandre Faure)

    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.