When applying for a job in quantitative finance, it is necessary to have read some basic books on the topics of mathematical finance or studied on an MFE course. Many of these books, such as Options, Futures and Other Derivatives ("Hull"), Financial Calculus ("Baxter & Rennie") and The Concepts and Practice of Mathematical Finance ("Joshi") are well known. However, there are some hidden gems that many do not look through, which can provide great insight into what occurs in a quant job. Here is a list of five books that don't often make the standard reading lists.
1) Mathematics for Finance: An Introduction to Financial Engineering (Springer Undergraduate Mathematics Series)
Mathematics for Finance is part of the Springer Undergraduate Mathematics Series and as such is a great introduction to the concepts of mathematical finance, from a more rigourous mathematical point of view. The level is geared towards a second or third year mathematics undergraduate. Proofs are included for results, as would be expected in a mathematics text, but the core quantitative finance results are retained. The book discusses both derivative pricing and briefly on modern portfolio theory, via the capital asset pricing model (CAPM). This book will make a great transitory text for the undergraduate pure mathematician who wishes to delve into the exciting world of mathematical finance.
Thomas Bjork has written an extremely comprehensive mathematical text on Arbitrage Theory in this book. As with Wilmott and Joshi, he follows the path of introducing the Binomial Model, then Stochastic Calculus and then finally derivative pricing via the Martingale approach. Once these chapters conclude, he spends time on many other areas of mathematical finance, including barrier option pricing, the LIBOR market model and early exercise options (optimal stopping times). It certainly provides a refreshing augmentation to the works of Joshi, Wilmott, Baxter & Rennie and Neftci, if more detail is required in particular areas. Further, there are helpful appendices on Measure Theory, Probability Theory and Martingales.
Although not a technical work, How I Became a Quant is a great bedside read for the aspiring financial engineer. It contains 25 accounts from quantitative individuals across a wide spectrum of Wall Street firms. Human interest stories on quantitative portfolio management, derivatives pricing, market microstructure and risk management are all covered. Don't expect a lot of technical detail on each individual's role, rather, see each story as a reflection on how they ended up in finance from backgrounds in mathematics and physics.
Rishi Narang has written up a great book about what to look for when investing in a quantitative fund. Pitched at the smart investor, the book provides a deep overview of all aspects of a systematic quantitative trading model and how to evaluate one. It discusses risk management from multiple points of view, including the perils of modelling and data management. Although the book is targeted at a non-technical individual evaluating a technical subject, it is equally valuable for a practicing quant trader or quant developer who works in a quant fund, wanting to improve their techniques and evaluate their risks in a more rigourous fashion.
Although not precisely one book, the "Effective" series by Scott Meyers could be considered one large book, split across three volumes. Many say that Effective C++ is required reading for a quantitative analyst - particularly a quantitative developer, writing up models in C++. This will unlikely be news to many. However, there are a great number of aspiring or practicing quants who decide to ignore the latter two books in the series, with obvious consequences. Meyers provides 85 more ways on top of the 55 found in Effective C++ to improve one's C++ programming, and in particular, one's use of the Standard Template Library. The STL contains many containers and algorithms, the majority of which are highly applicable to quantitative model development. If only to avoid re-inventing the wheel, it is worth reading this latter text.