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