I think part of the problem may be with using the parse path tool. The 'name' generated from the iterate tool doesn't actually create a pathname, it only creates a variable that holds the file name, so the parse path tool is probably creating nothing.
I've attached a image of a model that essentially does the same thing as yours, though it prompts the user to supply the name of a new folder, which it creates under the folder containing the raster data. If you needed the output folder in some other location alltogether you could give another parameter specifying the root directory for a new folder to get created in.
You have to use inline variables to string together the output folder name along with the raster name to create the raster dataset in this implementation.