They exist but are only sold through the Stansted Express website. £11 each way from Tottenham Hale or £12 from Liverpool Street or Stratford if booked at least 3 months in advance - more expensive if booked closer to the day of travel.It would be nice to see cheaper Advance options between London and Stansted, like on EMR to Luton or GWR to Gatwick (from Reading).
Because of the artificial retailing limitations GA have imposed, many people won't be aware of these fares.
The "Advance" fares that Heathrow Express and Stansted Express sell are not actually train-specific but just date-specific.There are many challenges involving airports and inflexible train tickets (e.g. reroutes or delayed flights) but plenty of passengers (me included!) would happily take these risks to save money on the rail fare.