Vintage Fritz Hansen Arne Jacobsen Swan Chair  

I can't help with authentication, but I can tell you that you're likely to get your head chewed off by another commenter for asking for valuation. For some reason, it's a big no-no.
Look at ebay and liveauctioneers.com for sold listings.

I am no Arne Jacobsen expert, but all the images I've seen of authentic Swan chairs do NOT show casters.  This makes me suspect that it is a knock-off.  
Of course, perhaps there was an authentic variation produced with casters.  I wouldn't know.  (I can say that If I were paying any more than knock-off prices, however, I would want to see proof that some authentic chairs were ever produced with casters).  

It all appears correct to me. I have a friend who owns one on a castor base. They are less common, but not unheard of.

I found a few old authentic ones with casters just by doing a quick google image search--including this one sold by Lauritz, the Danish auction house-
http://www.lauritz.com/en/auction/arne-jacobsen-lounge-chair-the-swan-ti...
Does yours tilt, too?  
 

It's real.
Like most things, a swan chair in poor condition has less value than one in very good condition.