  Excitons with large binding energies $\sim$2-3 eV in CrX$_{3}$ are
historically characterized as being localized (Frenkel) excitons that emerge
from the atomic $d{-}d$ transitions between the Cr-3$d$-$t_{2g}$ and $e_{g}$
orbitals. The argument has gathered strength in recent years as the excitons in
recently made monolayers are found at almost the same energies as the bulk. The
Laporte rule, which restricts such parity forbidden atomic transitions, can
relax if, at least, one element is present: spin-orbit coupling, odd-parity
phonons or Jahn-Teller distortion. While what can be classified as a purely
Frenkel exciton is a matter of definition, we show using an advanced first
principles parameter-free approach that these excitons in CrX$_{3}$, in both
its bulk and monolayer variants, have band-origin and do not require the
relaxation of Laporte rule as a fundamental principle. We show that, the
character of these excitons is mostly determined by the Cr-$d$ orbital
manifold, nevertheless, they appear only as a consequence of X-p states
hybridizing with the Cr-$d$. The hybridization enhances as the halogen atom
becomes heavier, bringing the X-$p$ states closer to the Cr-$d$ states in the
sequence Cl{\textrightarrow}Br{\textrightarrow}I, with an attendant increase in
exciton intensity and decrease in binding energy. By applying a range of
different kinds of perturbations, we show that, moderate changes to the
two-particle Hamiltonian that essentially modifies the Cr-$d$-X-$p$
hybridization, can alter both the intensities and positions of the exciton
peaks. A detailed analysis of several deep lying excitons, with and without
strain, reveals that the exciton is most Frenkel like in CrCl$_{3}$ and
acquires mixed Frenkel-Wannier character in CrI$_{3}$.
