Perhaps as many as 30 parallax microlensing events are known, thanks to the efforts of the MACHO, OGLE, EROS and MOA experiments monitoring the bulge. Using Galactic models, we construct mock catalogues of microlensing light curves towards the bulge, allowing for the uneven sampling and observational error bars of the OGLE-II experiment. The fraction of parallax events with delta chi^2 > 50 in the OGLE-II database is around ~1%, though higher fractions are reported by some other surveys. This is in accord with expectations from standard Galactic models. The fraction of parallax events depends strongly on the Einstein crossing time (t_E), being less than 5% at t_E = 50 days but rising to 50% at t_E > 1 yr. We find that the existence of parallax signatures is essentially controlled by the acceleration of the observer normalised to the projected Einstein radius on the observer plane divided by t_E^2. The properties of the parallax events - time-scales, projected velocities, source and lens locations - in our mock catalogues are analysed. Typically, ~38% of parallax events are caused by a disk star microlensing a bulge source, while ~33% are caused by a disk star microlensing a disk source (of these disk sources, one sixth are at a distance of 5 kpc or less). There is a significant shift in mean time-scale from 32 d for all events to ~130d for our parallax events. There are corresponding shifts for other parameters, such as the lens-source velocity projected onto the observer plane (~1110 km/s for all events versus ~80 km/s for parallax events) and the lens distance (6.7 kpc versus 3.7 kpc). We also assess the performance of parallax mass estimators and investigate whether our mock catalogue can reproduce events with features similar to a number of conjectured `black hole lens candidates.
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