According to German broker Lang & Schwarz, Traton shares have traded at a low of 29.25 euros ($33.3) to a high of 30.95 euros over the past week, although volumes are low.
Shares in the IPO are being offered at 27-33 euros.
Volkswagen aims to raise up to 1.9 billion euros (1.7 billion pounds) through the IPO, scaling back earlier ambitions to list up to a quarter of the unit by opting to float a 10% stake.
By 1213 GMT on Tuesday, shares in Traton were traded at 29.375 euros.
(Reporting by Danilo Masoni, editing by Louise Heavens)