If, for example, you write a parody of 'Streets of London', you are co-writer of a "derivative work". If all the words are your original work, you might be able to negotiate 50% royalties. Normally there will be some of the original lyrics, so your proportion of the royalties will be less.
The original composer of the song maintains 'moral rights' to the song, and thus has the right to refuse permission for his or her work to be used in a derivative work. This would apply whether your song was a parody or, for example, an 'answer song' like "Leave me alone , I like closed-down markets".
Cheers
Dave