  We developed a six-band $k \cdot p$ model that describes the electronic
states of monolayer transition metal dichalcogenides (TMDCs) in $K$-valleys.
The set of parameters for the $k \cdot p$ model is uniquely determined by
decomposing tight-binding (TB) models in the vicinity of $K^\pm$-points. First,
we used TB models existing in literature to derive systematic parametrizations
for different materials, including MoS$_2$, WS$_2$, MoSe$_2$ and WSe$_2$. Then,
by using the derived six-band $k \cdot p$ Hamiltonian we calculated effective
masses, Landau levels, and the effective exciton $g$-factor $g_{X^0}$ in
different TMDCs. We showed that TB parameterizations existing in literature
result in small absolute values of $g_{X^0}$, which are far from the
experimentally measured $g_{X^0} \approx -4$. To further investigate this issue
we derived two additional sets of $k \cdot p$ parameters by developing our own
TB parameterizations based on simultaneous fitting of ab-initio calculated,
within the density functional (DFT) and $GW$ approaches, energy dispersion and
the value of $g_{X^0}$. We showed that the change in TB parameters, which only
slightly affects the dispersion of higher conduction and deep valence bands,
may result in a significant increase of $|g_{X^0}|$, yielding
close-to-experiment values of $g_{X^0}$. Such a high parameter sensitivity of
$g_{X^0}$ opens a way to further improvement of DFT and TB models.
