Max Key's intimate holiday video

Max Key and his girlfriend in Hawaii. Photo / Youtube

Max Key has posted a video in which he flaunts his jet-setting, perfectly tanned lifestyle with model girlfriend Amelia Finlayson - but there's no hint of a marriage proposal.

The Prime Minister's son uploaded the video to YouTube tonight, two days after he posted a teaser photo to Instagram, sparking rumours of a proposal.

The Instagram photo showed the couple holding hands and gazing into each other's eyes on a Hawaiian volcano.

But while the "summer paradise" video doesn't feature a proposal, it does show the couple gallivanting about in New Zealand and Hawaii - often with Amelia in a bikini and Max eschewing a shirt.

Max described the video as a "journey into myself and Amelia's teenage years, filmed over the last few months".

In one shot, Amelia blows a kiss into the camera. In another, Max hits the surf.

The video also shows the couple - often holding hands - on beaches, in the bush, at a waterfall swimming hole, on a launch in clear blue water, and snorkelling.

Max's hot pink-haired sister Stephie and his dad John - wearing a pair of sunnies - also make brief appearances in the video.