I am currently a physics & math undergraduate interested in quantitative finance. I have taken computational math up to PDEs, proofs-based math up to linear algebra, and am currently taking graduate physics courses (I am saying this so you can get a feel for my background). I was wondering if there was a book (or books) recommended for my situation. Most of the books I've seen recommended on here, or from other searches I've made, seem to be in one of two camps:
- They are incredibly basic (e.g. "Here's what a Taylor series is..."), and move very slowly through the the (not very mathematical) theory presented in the book. Books like these seem kind of boring to me, if I'm being honest. An example of this that comes to mind is Hull's book.
- They are advanced statistics/stochastic calculus books, or are for people "in the industry". For the first case, I can usually follow what they're saying in a strictly mathematical sense, but I wonder about the applications of such a treatment of the subject (I would guess this is because I don't have the context for judging what's a useful treatment, and I also don't have any immediate use for the tools developed). Alternatively, if they're meant for people in the industry, the assumed background of previous knowledge makes the material too advanced to follow comfortably (i.e. I feel like I just have to take it "as is"; that is, not relating it to other subjects, or grounding it in previous knowledge). After reading a chapter of such a book, I could probably convince someone that I know something about what I just read (throwing out terminology, citing examples, etc.), but I personally wouldn't feel comfortable with my understanding. An example of this is Taleb's Dynamic Hedging.
I was wondering if there was a book that, while being somewhat introductory (not assuming much background in terms of previous finance vocabulary or experience), wasn't afraid of putting more advanced math in its text. Also, I would strongly prefer books with exercises in them; I know from previous experience that reading theory without doing exercises is quite harmful to your development in a subject. I'm aware this question may seem lazy or repetitive, as there are multiple book recommendations already out there, (e.g. this booklist, or this one), but for the previously mentioned reasons, I was curious to see if there were more specific suggestions. I also have zero context on the industry, so important distinctions like arbitrage theory vs. credit derivatives mean literally nothing to me; this makes it difficult to decide what I should do/read to learn more (which makes big booklists not very helpful to me at the moment). Thanks in advance!
Edit: the book I settled on is Thomas Mazzoni's "A First Course in Quantitative Finance". It's quite mathematical, has exercises with solutions, and covers interesting material.