Advanced Search
MyIDEAS: Login to save this paper or follow this series

Ito Processes with Finitely Many States of Memory


Author Info

  • McCauley, Joseph L.
Registered author(s):


    We show that Ito processes imply the Fokker-Planck (K2) and Kolmogorov backward time (K1) partial differential eqns. (pde) for transition densities, which in turn imply the Chapman-Kolmogorov equation without approximations. This result is not restricted to Markov processes. We define ‘finite memory’ and show that Ito processes admit finitely many states of memory. We then provide an example of a Gaussian transition density depending on two past states that satisfies both K1, K2, and the Chapman-Kolmogorov eqn. Finally, we show that transition densities of Black-Scholes type pdes with finite memory are martingales and also satisfy the Chapman-Kolmogorov equation. This leads to the shortest possible proof that the transition density of the Black-Scholes pde provides the so-called ‘martingale measure’ of option pricing.

    Download Info

    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:
    File Function: original version
    Download Restriction: no

    Bibliographic Info

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 5811.

    as in new window
    Date of creation: 16 Nov 2007
    Date of revision:
    Handle: RePEc:pra:mprapa:5811

    Contact details of provider:
    Postal: Schackstr. 4, D-80539 Munich, Germany
    Phone: +49-(0)89-2180-2219
    Fax: +49-(0)89-2180-3900
    Web page:
    More information through EDIRC

    Related research

    Keywords: Ito process; martingale; stochastic differential eqn.; Langevin eqn.; memory; nonMarkov process; Fokker-Planck eqn.; Kolmogorov’s backward time eqn.; Chapman-Kolmogorov eqn.; Black-Scholes eqn;

    Find related papers by JEL classification:

    This paper has been announced in the following NEP Reports:


    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. McCauley, J.L. & Gunaratne, G.H. & Bassler, K.E., 2007. "Martingale option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 380(C), pages 351-356.
    2. McCauley, Joseph L. & Gunaratne, Gemunu H. & Bassler, Kevin E., 2007. "Martingale option pricing," MPRA Paper 2151, University Library of Munich, Germany.
    3. Duffie, Darrell, 1988. "An extension of the Black-Scholes model of security valuation," Journal of Economic Theory, Elsevier, Elsevier, vol. 46(1), pages 194-204, October.
    4. J. L. McCauley & G. H. Gunaratne & K. E. Bassler, 2006. "Martingale Option Pricing," Papers physics/0606011,, revised Feb 2007.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:
    1. Bassler, Kevin E. & Gunaratne, Gemunu H. & McCauley, Joseph L., 2007. "Empirically Based Modeling in the Social Sciences and Spurious Stylized Facts," MPRA Paper 5813, University Library of Munich, Germany.


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


    Access and download statistics


    When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:5811. 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: (Ekkehart Schlicht).

    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.