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In order to estimate the effects of local structure on the Hubble parameterwe calculate the low-redshift expansion for $H(z)$ and $\frac{\delta H}{H}$ foran observer at the center of a spherically symmetric matter distribution inpresence of a cosmological constant. We then test the accuracy of the formulaecomparing them with fully relativistic non perturbative numerical calculationsfor different cases for the density profile. The low red-shift expansion weobtain gives results more precise than perturbation theory since is based onthe use of an exact solution of Einstein's field equations. For larger densitycontrasts the low red-shift formulae accuracy improves respect to theperturbation theory accuracy because the latter is based on the assumption of asmall density contrast, while the former does not rely on such assumption.  The formulae can be used to take into account the effects on the Hubbleexpansion parameter due to the monopole component of the local structure. Ifthe $H(z)$ observations will show deviations from the $\Lambda CDM$ predictioncompatible with the formulae we have derived, this could be considered anindependent evidence of the existence of a local inhomogeneity, and theformulae could be used to determine the characteristics of this localstructure.

Low red-shift effects of local structure on the Hubble parameter in presence of a cosmological constant