Exploratory semiparametric analysis of two-dimensional diffusions in finance

Cristian Huse and Renato Flôres Junior

No 371, FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) from EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil)

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.

Date: 2000-03-01
References: Add references at CitEc
Citations:

Downloads: (external link)
https://repositorio.fgv.br/bitstreams/c3df4147-cb8 ... f0e41ab6d76/download (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:fgv:epgewp:371

Access Statistics for this paper

More papers in FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) from EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil) Contact information at EDIRC.
Bibliographic data for series maintained by Núcleo de Computação da FGV EPGE ().