  The analysis of cosmological galaxy surveys requires realistic simulations
for their interpretation. Forward modelling is a powerful method to simulate
galaxy clustering without the need for an underlying complex model. This
approach requires fast cosmological simulations with a high resolution and
large volume, to resolve small dark matter halos associated to single galaxies.
In this work, we present fast halo and subhalo clustering simulations based on
the Lagrangian perturbation theory code PINOCCHIO, which generates halos and
merger trees. The subhalo progenitors are extracted from the merger history and
the survival of subhalos is modelled. We introduce a new fitting function for
the subhalo merger time, which includes a redshift dependence of the fitting
parameters. The spatial distribution of subhalos within their hosts is modelled
using a number density profile. We compare our simulations with the halo finder
ROCKSTAR applied to the full N-body code GADGET-2. The subhalo velocity
function and the correlation function of halos and subhalos are in good
agreement. We investigate the effect of the chosen number density profile on
the resulting subhalo clustering. Our simulation is approximate yet realistic
and significantly faster compared to a full N-body simulation combined with a
halo finder. The fast halo and subhalo clustering simulations offer good
prospects for galaxy forward models using subhalo abundance matching.
