There will be many here who are much more experienced in the nuances of what determines market price.
In my understanding these would be the key variables (one may outweigh another depending on sword)
Age of blade - koto>Shinto>shinshinto
Popularity of school/maker (there is a heirarchy)
Condition/attributes of blade - ubu, suriage, signed, nengo, cutting test, polish
Papers attained (Juyo + will generally not go below a certain price as stated above)
Provenance (daimyo owned etc)
As to how important each variable is in relation to each other is where nuance and experience comes in