The dollar climbed past more of last year's peaks against the euro on Thursday, with only the March 2015 high of $1.0457 standing in the way of a push towards parity that banks are again saying is on the cards.

With U.S. markets out for the Thanksgiving holiday, trade is expected to be thinner, and the dollar set a series of new landmarks in early trade in Europe, extending its surge after another strong batch of U.S. economic data on Wednesday.