https://alo.mit.edu/wp-content/uploads/2017/06/The-Statistic...
I have a hard time finding courses or books that cover how these instruments work in some depth.
Here we go anyway:
Hull: Futures, Options, and Other Derivatives
Natenberg. Don't recall the name, but this is maybe the closest to practical.
Paul Wilmott, Quantitative finance.
Taleb, Dynamic Hedging. Got a signed copy :)
Also I think it's smart to read about instruments that aren't options, ie don't just cut to the chase. Time value of money, futures, forwards, bonds, swaps, equities. Then vanilla options on all those things, then exotics.
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.
Interesting comment about the math. For my physics degree, a lot of times it was easier to think about things once I understood more of the math. I’ll see how it goes here.
If you're selling options, you probably need to risk adjust your returns a bit more than what's common:
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=377260
That's by Andrew Lo, big name in the area.
I'm sure you've also come across Taleb, who knows a thing or two about selling options.