
"The step-by-step approach of this book makes it one of the most accessible and popular explanations of the mathematical models used to price derivatives. For the Second Edition, Salih Neftci has thoroughly expanded one chapter, added six new ones, and inserted chapter-concluding exercises. He does not assume that the reader has a thorough mathematical background, and the math is lucid and fresh. His explanations of financial calculus are remarkable for their simplicity and perception."--BOOK JACKET.
But there are attempts at it. Most notable are:
- "An Introduction to the Mathematics of Financial Derivatives", by Neftci
- Wilmott books aren't bad.
- Brigo's "Interest Rate Models" is... flaky. It is a lot of material and seems to be quite rigorous, until some point most crucial for understanding, which gets skipped over. The interviews with traders at the end are good.
- Only buy Choudhry books, if you want to talk good about finance.
Lecture notes from Dr Kohn at NYU: http://www.math.nyu.edu/faculty/kohn/math-finance-lecture-no...
Options, Futures, and Other Derivatives by Hull (considered one of the best books in this field, but I like the next one better)
An Introduction to the Mathematics of Financial Derivatives by Neftci
Numerical Methods in Finance and Economics: A MATLAB-Based Introduction (Statistics in Practice) by Brandimarte
Also, we take a general C++ course. Coming into the program they wanted us to have completed math through calc 3, differential equations (first course), and linear algebra (first course). I was a finance undergrad not math, so from experience I can say I wish I would have also studied some real analysis (just the basics), and a high level undergrad course in probability (although we took a grad level intro course first semester). Also, the better you are at proofs, the easier time you will have (I had no training in this and have picked it up as we go along).
Also, some schools make a distinction between computational finance and mathematical finance, so that's something to think about too.