Houdini's fireworks have an inherit color, which is the attribute called Cd. This needs to be passed the Arnold shader network to be used.
Under the attached Arnold properties is a tab called Attributes. Clicking the down arrow next to Point Attributes will list the available attributes on the fireworks, choose Cd. This will pass the attribute to the .ass file as User Data.
Now the disks should be rendered with color.
At the moment the Particles are being rendered as flat colored disks but they could be rendered as spheres with volume.
Render the scene again.
It is very dull because the values being passed to the Standard Volume are very low. Insert a Multiply node and set Input2 to 40.
Close up, the volumetric nature of the spheres can be seen.
The resulting scene from this section can be downloaded below.