Whenever the topic comes up, I throw out a reference to Hull's Futures, Options and other derivatives, Wilmott's Quantitative Finance, and possibly also Taleb's Dynamic Hedging.

That's more than enough on the instrument math side, most of what you'll see is pretty mundane stuff, unless you end up on an exotics structuring desk.

I'd also note that JS and other MMs mostly don't do anything requiring you to know the intimate details of these things, a lot of it is understanding how the market works rather than the deep instrument math. That might mean other kinds of math of course.

My writeup: https://keithalewis.github.io/math/um.html for modeling and https://keithalewis.github.io/math/uf.html on now to more accurately reflect the real world. I have taught Derivative Securities at NYU, Columbia, Cornell, and Rutgers over the past 14 years, but my day job is turning math into software that produces numbers people running a business will pay for. The textbooks are missing some important things.

Nicely organized and dense.

Thanks for the material!

Hull's Futures, Options and other derivatives was on the bookshelf of a friend who worked at JS - it was their bible.

I always throught market microstructure was more important, but they insisted a disciplined application of the maths (as per the bible of Hull) was where the magic really was.

If you come from a pure math theory first background I would advise starting out with Björks “Arbitrage theory in continuous time”, I personally found the lack of rigor and superfluous examples in Hull frustrating and found Björk much more approachable then you can look into Hull for real life practicalities like daycount conventions, etc. If you want to go into complex derivatives pricing I would advise looking at the Andersen and Piterbarg trilogy.

I would also suggest to forget about Hull and Wilmott and would suggest to start with the excellent book by Shreve: "Stochastic Calculus for Finance. Volume II: Continuous Time Models".

Then, you can quickly read Bjoerk, work through Brigo/Mercurio (if you like that style) or Andersen/Piterbarg. Alternatively, if you want to fully dive into into the subject after Shreve, Musiela/Rutkowski: "Martingale Methods in Financial Modelling" is wonderful.

I'd say that Shreve and Musiela lack rigour and are too focused on trivia, name-dropping and anecdotes. Jiao's "Infinite-dimensional methods in amassing vast bags of gold" is unsurpassed. For its coverage of Black-Scholes, I'd also recommend Schulz's "Good Grief, Charlie Brown". Sorry, everyone seemed to be doing this so I felt I should contribute too.

I honestly can't tell exactly when the thread meandered into satire.

This. Exactly this.

Thank you kindly for what looks like a great resource!

I've been trying to put myself through YouTube night school on some of this stuff, and MIT OCW has great resources as well at significantly less cost than going to MIT ;)

This is a pretty reasonable jumping off point for their corpus of financial engineering stuff: https://www.youtube.com/watch?v=HdHlfiOAJyE.

I'm fortunate enough to work with a person who actually understands derivatives trades with some sophistication, but that's a happy accident and the more people have access to good online resources the better!

Edit: I forgot to mention this book (https://www.amazon.com/Algorithmic-Trading-DMA-introduction-...) in the spirit of something more technical than the general-audience one I linked above. I have some nitpicks with it as well, but I've gotten value out of it.

Followed quantpy tutorials to implement my own black scholes and heston pricing models last year. Highly recommend.