The correct option is A Future Perfect Continuous
Here, 'will have been writing' indicates Future Perfect Continuous. It is
used to indicate an action that will have happened for some time and will not
be complete yet at a certain point in the future.
Future Continuous (will be writing) indicates
what will be going on in the near future.
Present Perfect Continuous (have been writing) is
used to indicate an action that started at some point in the past and may or
may not be complete.
Present Perfect (have written) is
used to indicate an action which started in the past and has continued up
untill now.