Use "Contextual Filter" value as relative date for exposed filter

I would like to have the date value that comes from a contextual filter (argument of a view page display) as the default value for the exposed filter. The only options I see are: "Select a date" or "Enter a relative date" where relative maybe some PHP date.

Example: page/2011-11-08 -> use 2011-11-08 as default value for exposed filter.

Is there a way to achieve this?