How can I get a loud noise out of a 15mm piezo disc?
Loud sound comes from using more voltage on the disk, driving it at the mechanical resonant frequency and mounting it properly (no contact with the disk other than at the mechanical node(s) in an accoustically resonant cavity with the proper size hole. 

In a typical bender disk (oilcan resonant mode) the mounting is typically something like a circular knife edge at the null. Contact away from the null point will damp the resonance, reducing the mechanical Q and thus the sound volume.  

You can get more voltage by using a step-up transformer or inductor, or use a boost converter to generate a higher voltage rail and then use an amplifier (the latter would probably be more compact because the boost converter could operate at much higher frequency so the magnetics could be made much smaller).