Why do you want to update the BIOS? Updating, or Flashing, the BIOS is usually done to correct bugs or to increase compatibility (for example, to add support for newer processors). Since this is a laptop, your upgrade options are limited to adding more RAM, replacing the HDD/SDD and optical drive. Generally speaking, none of these changes require a BIOS flah/upgrade.
Unless specifically mentioned on the available downloads for your particular model, a BIOS upgrade is not currently available. Having checked the available downloads for the VGN-FZ31Z
laptop, I can't find anything as regards upgrading your BIOS. Sorry.
VAIO Support Europe