The grace period whether here or in the US always starts when the student is no longer enrolled at least half time.
Once students cease academic activity, they are considered as the equivalent of "Graduated" regardless of the date of parade on stage.
In the case of US Federal loans for Postgraduate Students the date of submission of their thesis is the end of their academic activity so their grace period begins from then and not after the conferring ceremony the following January.
Undergraduate students are reported as graduated once the spring semester results are released in mid June.