In ArcGIS 10.1 (advanced license), I have a DTM representing a small island. Of course, off-coast cells are given NoData. Now, I would like to have those off-coast areas set to 0, i.e. sea level. I used raster calculator (with a conditional statement) to set the NoData cells to 0, leaving unchanged the land cells. The problem with that is that the sea level is limited to the extent of the raster, but I would like to have a larger portion of sea "represented" (i.e., well outside the raster's extent).
It sounds like a simple (and dirty) solution would be to change the colour of the map canvas (what is referred to as the Data Frame) to match the No data value. This can be done in ArcMap.
If you wanted to manipulate the raster data itself I would suggest creating an adjacent raster tile and pad with zero, or a no data value. I have detailed the creation of a 5k 'Sea Tile' on another question, which might be of use here - Adding blank rasters to mosaic in ArcGIS Desktop?