It's very much impossible to say anything about the budget unless you state at least the most basic requirements such as:
- niche / content description
- quantity / start up + updates
- exclusive / non exclusive
Also, I asssume that by "studio" you do mean an actual "producer", as studio in the typical sense of the term means a brand that is marketed to consumers.
Although some of the biggest studios do have in house content production department, most outsource their content to third party producers.
Anyway, if you are serious about content I would recommend to check out
www.amazingcontent.com for licensing and custom exclusive production alike.