The permissions to moderate Answers are granted by your Karma level.
https://answers.atlassian.com/faq/
Currently the requirement is 2000 karma for the admin rights to close your own issue (I believe this is subject to adjustment at a later time).
Until you build up your karma score, if you no longer need an answer to your question, you can add a comment to your post and it will be closed out.
Sorry, I think the hike to 2000 karma points was my fault because I asked if the FAQs could include the usage of 'Closed' after stumbling across this question
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