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Can anyone recommend books that explain the math used in quantitative finance academic papers?

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    $\begingroup$ You should be more specific about the kind of paper you want to read. Like are you interested in Fixed Income, Equity derivatives, Market Making, Behavioral Finance? I mean, you question is a bit like if I went to a library and asked for a book helping me understand "sports on TV". $\endgroup$ – SRKX Sep 27 '11 at 7:04
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    $\begingroup$ This should be closed. Clearly a pooling question of the “What’s your favorite ______?” type. $\endgroup$ – Ryogi Oct 31 '11 at 18:17
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    $\begingroup$ @RYogi Ultimately I think this question was worth keeping, even if only to point out to future beginner questioners looking to learn. After all, this question just keeps popping up, and ultimately it may even be useful for experienced quants to see what others are reading. $\endgroup$ – Tal Fishman Dec 16 '11 at 9:42
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    $\begingroup$ Perhaps we could add more questions for books in specific topics, eg. fixed income securities, interest rate securities, options, etc etc. The lists of books below are generally very broad-based and not narrow enough. $\endgroup$ – user1796 Dec 19 '11 at 14:00
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    $\begingroup$ @EX10NY The same books listed below generally cover many of those (still relatively broad) topics. Taken together, you can certainly get a sense for what to read in any quant finance topic from the answers below. If you want truly narrow, ask a very specific question. There have been a few of those here in the past where I've recommended a specific book. $\endgroup$ – Tal Fishman Dec 23 '11 at 14:38
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If you need a primer covering various domains of math then Dan Stefanica's text will do the job. The text covers multivariable calculus, lagrange multipliers, black scholes PDF, greeks & hedging, newton's method, bootstrapping, taylor series, numerical integration, and risk neutral valuation. It also includes a mathematical appendix.

If you want an introduction to risk analysis complete with geometric interpretations check out ATillio Meucci's Risk and Asset Allocation.

Hull's Options, Futures, and Derivatives is a classic that includes stochastic calculus and the topics in the title.

Here are the best applied statistics books:

Rene Carmona's "Statistical Analysis of Financial Data in S-Plus" covers a lot of ground with examples compatible with R. He starts with foundations and builds towards more complex models.

If you want ready-to-apply solutions Eric Zivot's "Modeling Financial Time Series with S-Plus" is encyclopedic in the range of topics covered. Whereas Carmona will focus on various modeling techniques, Zivot will cover portfolio optimization, factor analysis, and many other topics. It makes for a great reference rather than a cover-to-cover read.

If you want to focus on time-series specifically with an applied bent - Shumway and Stoffer's Time Series Analysis and Applications is also great. The solutions are compatible with R.

There are various theoretical statistics books (Hamilton, Ruey Tsay) but those will assume you understand the math.

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    $\begingroup$ Attilio Meucci's book is very good. $\endgroup$ – lehalle Jan 16 '14 at 7:06
  • $\begingroup$ John Cochrane's 'Asset Pricing' is certainly the book to acquire some quantitative insights into asset pricing $\endgroup$ – Tim Apr 1 '16 at 16:07
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I doubt you will find one book that covers everything you need, but here are a few that I continually come back to whenever I have some questions on the mathematics.

A few previous questions also have some good recommendations contained within their answers. See here and here.

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If you asked me for a single book as a starting point I'd probably go for:

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  • $\begingroup$ +1 for that one because I really like it, but it's not sufficient to learn. $\endgroup$ – SRKX Sep 27 '11 at 6:59
  • $\begingroup$ @SRKX: I agree, but it's a good starting point because it also gives lots of references where to continue. I chose this because the question is really, really broad. $\endgroup$ – vonjd Sep 27 '11 at 7:13
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    $\begingroup$ haha see my comment on the question... $\endgroup$ – SRKX Sep 27 '11 at 7:23
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I'd say to read Prof. Shreve's well-known two-volume textbook Stochastic Calculus for Finance I and II.

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All books recommended in previous posts are splendid :-) I would like to add one more book for continuous time financial mathematics: Arbitrage Theory in Continuous Time by Tomas Bjork.

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Paul Wilmott on Quantitative Finance.

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Some more references. Here are three starting books:

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I recommend to you : "Market Risk Analysis" by Alexander Carol for the "finance" part and "Time Series Analysis" by Hamilton for the "maths/stats" part;

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