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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.

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    $\begingroup$ I also have zero context on the industry, so important distinctions like arbitrage theory vs. credit derivatives mean literally nothing to me. Might it be helpful to study some finance before proceeding to quantitative finance? $\endgroup$ Feb 15 at 19:03
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    $\begingroup$ Going further, I would say that if you are not interested in economic or money questions generally (eg. why is the price of apples what it is) then you probably won't find quantitative finance very interesting. Which is fine, different people are interested in different things. $\endgroup$
    – nbbo2
    Feb 16 at 9:19
  • $\begingroup$ @RichardHardy Yes, that sounds pretty reasonable. Sharad recommended Investment Science, which looks nice. Do you have any other recommendations? $\endgroup$
    – wlancer
    Feb 16 at 16:10
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    $\begingroup$ @nbbo2 I certainly wasn't saying this, but I supposed someone could have inferred it from my tone in the post. I do think this stuff is interesting, but I haven't really gotten into it yet. I think a clarification would be that, while I think finance is interesting, I think the idea of applying math (and possibly physics-esque ideas) to finance is more interesting. Anyway, thanks for the comment! $\endgroup$
    – wlancer
    Feb 16 at 16:12

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It's hard to find a book that strikes the balance you seek but, to build on Richard Hardy's suggestion, I would recommend a textbook that provides an introduction to finance while not shying away from the mathematical modeling involved in setting up the fundamental problems. I recommend David Luenberger's text: Investment Science: it is very lucidly written, has solid coverage of the key areas, and also has a nice selection of exercises. While it may not be as mathematically intense as you might like, I found it very helpful in developing solid intuition for the fundamentals.

A more high-speed route but one that I didn't find as useful in deepening my understanding is Stephen Blyth's "An Introduction to Quantitative Finance."

Finally, "Financial Calculus" by Baxter and Rennie offers a brief and accessible path to understanding some of the stochastic calculus behind the pricing and construction of derivative securities. Nice exercises too!

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I think Paul Wilmott $\underline{on}$ Quant Finance is suitable for you. Not Paul Wilmott Introduces Quant Finance - that sounds a bit too simple for you.

You can also try this recently updated post: A good book on option pricing from theoretical and practical aspect

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  • $\begingroup$ Thank you for this recommendation. Do you know a place I could find exercises to test the theory taught in this book? $\endgroup$
    – wlancer
    Feb 16 at 16:17

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