IDEAS home Printed from https://ideas.repec.org/p/fgv/epgewp/371.html
   My bibliography  Save this paper

Exploratory semiparametric analysis of two-dimensional diffusions in finance

Author

Listed:
  • Huse, Cristian
  • Flôres Junior, Renato Galvão

Abstract

We examine bivariate extensions of Aït-Sahalia’s approach to the estimation of univariate diffusions. Our message is that extending his idea to a bivariate setting is not straightforward. In higher dimensions, as opposed to the univariate case, the elements of the Itô and Fokker-Planck representations do not coincide; and, even imposing sensible assumptions on the marginal drifts and volatilities is not sufficient to obtain direct generalisations. We develop exploratory estimation and testing procedures, by parametrizing the drifts of both component processes and setting restrictions on the terms of either the Itô or the Fokker-Planck covariance matrices. This may lead to highly nonlinear ordinary differential equations, where the definition of boundary conditions is crucial. For the methods developed, the Fokker-Planck representation seems more tractable than the Itô’s. Questions for further research include the design of regularity conditions on the time series dependence in the data, the kernels actually used and the bandwidths, to obtain asymptotic properties for the estimators proposed. A particular case seems promising: 'causal bivariate models' in which only one of the diffusions contributes to the volatility of the other. Hedging strategies which estimate separately the univariate diffusions at stake may thus be improved.

Suggested Citation

  • Huse, Cristian & Flôres Junior, Renato Galvão, 2000. "Exploratory semiparametric analysis of two-dimensional diffusions in finance," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 371, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
  • Handle: RePEc:fgv:epgewp:371
    as

    Download full text from publisher

    File URL: https://repositorio.fgv.br/bitstreams/c3df4147-cb88-4d6c-b5ae-ff0e41ab6d76/download
    Download Restriction: no
    ---><---

    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:fgv:epgewp:371. 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: Núcleo de Computação da FGV EPGE (email available below). General contact details of provider: https://edirc.repec.org/data/epgvfbr.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.