  We present results of an all-sky search in the Parkes Pulsar Timing Array
(PPTA) Data Release 1 data set for continuous gravitational waves (GWs) in the
frequency range from $5\times 10^{-9}$ to $2\times 10^{-7}$ Hz. Such signals
could be produced by individual supermassive binary black hole systems in the
early stage of coalescence. We phase up the pulsar timing array data set to
form, for each position on the sky, two data streams that correspond to the two
GW polarizations and then carry out an optimal search for GW signals on these
data streams. Since no statistically significant GWs were detected, we place
upper limits on the intrinsic GW strain amplitude $h_0$ for a range of GW
frequencies. For example, at $10^{-8}$ Hz our analysis has excluded with $95\%$
confidence the presence of signals with $h_0\geqslant 1.7\times 10^{-14}$. Our
new limits are about a factor of four more stringent than those of Yardley et
al. (2010) based on an earlier PPTA data set and a factor of two better than
those reported in the recent Arzoumanian et al. (2014) paper. We also present
PPTA directional sensitivity curves and find that for the most sensitive region
on the sky, the current data set is sensitive to GWs from circular supermassive
binary black holes with chirp masses of $10^{9} M_{\odot}$ out to a luminosity
distance of about 100 Mpc. Finally, we set an upper limit of $4 \times 10^{-3}
{\rm{Mpc}}^{-3} {\rm{Gyr}}^{-1}$ at $95\%$ confidence on the coalescence rate
of nearby ($z \lesssim 0.1$) supermassive binary black holes in circular orbits
with chirp masses of $10^{10}M_{\odot}$.
