  We present a new Monte Carlo code for Comptonisation in Astrophysics (MoCA).
To our knowledge MoCA is the first code that uses a single photon approach in a
full special relativity scenario, and including also Klein-Nishina effects as
well as polarisation. In this paper we describe in detail how the code works,
and show first results from the case of extended coronae in accreting sources
Comptonising the accretion disc thermal emission. We explored both a slab and a
spherical geometry, to make comparison with public analytical codes more easy.
Our spectra are in good agreement with those from analytical codes for
low/moderate optical depths, but differ significantly, as expected, for optical
depths larger than a few. Klein-Nishina effects become relevant above 100 keV
depending on the optical thickness and thermal energy of the corona. We also
calculated the polarisation properties for the two geometries, which show that
X-ray polarimetry is a very useful tool to discriminate between them.
