Are you a trader?

I second Trading and Exchanges, a phenomenal overview for folks who want to learn how brokerages and market making work.

What would one need to fully understand before tackling these books? What field would these books help them understand and apply this knowledge in?

Having used both Hull and Shreve in two different courses I'd say they're aimed at very different audiences. The course I took using Shreve didn't actually teach much about real world "options, futures, and other derivatives", but treated them more like abstract mathematical ideas and focused more on the mathematical theory used to model such contracts. While the course using Hull focused more on those contacts, not as abstract mathematical concepts, but as real things that actually exist and are actually traded by real people in the real world with all the messiness and uncertainty that can entail. Admittedly a large part of this was no doubt due to the Shreve based course being taught by the math department and the Hull based course being taught be economics department

While I on many levels preferred the Shreve based course, if I had to pick one for practitioners working day to day with this stuff (which I don't actually do, despite my degree), I'd definitely pick Hull.

Optional types and futures are both important and useful examples of monads—in the “container” and “action” interpretations, respectively; and derivatives are the method of constructing zippers, which are an accessible example of comonads, as well as a useful method of constructing other things like parsers, so these are actually pretty solid concepts for a functional programmer—whether in Haskell or otherwise. I would totally buy that book. :)

What did you study? How did you apply the knowledge in the book?