I think that given the question about "how these instruments work in some depth" Hull is more appropriate.

This was indeed what I was getting at! Good to have a Stochastic book recommendation anyway, might also be i teresting. :)

What does "strong math background" mean in this context? Would the equivalent of an undergrad degree in math be sufficient, or are we talking about graduate level analysis and stats here?

> Björk: Arbitrage Theory in Continuous Time

is standard graduate stochastic calculus course material. An undergrad degree in math usually specializes in a certain track: algebra or analysis. The analysis background would be a closer fit as the material is focused on the continuous applications (not HFT) and likely have covered the introductory measure and probability theory material. The finance portion focuses on the arbitrage-risk neutral model that is at least a semester worth a material.