I have tried to check the graphics options but I can't see any HDR settings there... do I need a specific graphics card? I have a GeForce GTX 1070.

I think that Since patch 1.03 it should work by default if your computer (GPU, OS, Processor and monitor) supports HDR, but I have no confirmation on that.

EDIT: I just reinstalled the game. There actually is HDR setting on the graphics settings.
Check that the game is updated and that HDR is configured in Windows 10.
https://support.microsoft.com/en-us/help/4040263/windows-10-hdr-advanced-color-settings

Pretty sure the 1070 does not support HDR--as it predates the GPUs that do. Basically, with AMD it's the RX-5000-series and newer that support it, and with nVidia it's the RTX-2000 series and newer that support HDR. Earlier cards do not.

Also, there is a 3d API option in D3d versions and elsewhere that has been around for a long time also called "hdr" unfortunately...;) High Dynamic Range in the old days does not mean what it means today...! Also, it's not just HDR hardware, but how well the game software supports HDR is a huge factor. Some HDR games look terrible--washed out, so bad you immediately want to turn HDR off. But some games do a fantastic job with HDR--RDR2 does a very good job with it, and so does No Man's Sky (latest patches and versions), but the best HDR I've ever seen in a game with my 5700XT is Baldur's Gate 3--at 4k HDR it is drop-dead gorgeous--it's my default for running the game--looks noticeably superior to the standard non-HDR display, imo.

Hi,

just a quick message to add that a Geforce GTX1070 does actually support HDR. (Nvidia's cards have been supporting the mode ever sice the 900-series). I'm playing the game with that card myself.

You need to make sure you have set the game to 'true' Fullscreen-mode in order to activate the HDR-option and gain access to its settings.