This is the 'Elements of Style' for Quantitative Finance: compact, style-setting, purposeful, and designed for the new learner. This book shouldn't be necessary: it reviews basic material that is elsewhere covered by bookshelves (library wings?) full of larger texts on the same topics. Instead, what's amazing is that it can replace an entire bookshelf of larger texts; it is that well-crafted.
The *style* is unique and ought to become the standard against which finance texts are judged. Unlike most finance texts, it does not meander. It is written by a teacher for new learners. Clearly, the author has put great care into the choices. Also clearly, the editing is superb. Like Hering Cheng, I have read it cover to cover. Nary a page is wasted. As finance texts goes, I find it simply delicious in elegance and economy of presentation. Served like a fine dish by a master chef who sweated every detail in the kitchen. The recipe may be lasagna (been there, done that) but still...the best lasagna.
The details, for example. Keywords emphasized in italics. Carefully considered hierarchical organization (e.g., I.3.3.2. It takes time to do this right). Language precision; e.g., a footnote that distinguishes analytic from closed-form, discussion on arithmetic/geometric Brownian motion that often stumps new learners but is often ignored in texts.
The book is informed by actual teaching, as it seems to anticipate many new learning hurdles. It is the first finance text I've read where the reader is not led down any big, blind alleys. Finance texts love to occasionally abandon new learners with an abrupt, intimidating formula. Prof. Alexander cares more than that. Important ideas concepts have concrete, actionable, workable examples. From start to finish, the text supports self-study (except, maybe just maybe, the matrices/eigenvalues may ask for a bit of outside help).
Regarding the criticism for using Excel: they are silly. Excel is the only correct choice for the audience. It is the only common denominator. Otherwise, the only way to meet the audience with examples is to show every example in three or four software code version. This is not necessary for an introduction, excel is the economical choice. And, btw, unlike most finance texts, the Excel worksheets are prepared with care; e.g., the regression XLS has embedded screenshots of the necessary add-in menus. Let us celebrate the lost art of attention to detail.
In regard to topics, book contains:
* Basic calculus and linear algebra (some of the building blocks that are so necessary to understanding complex instruments). The book comfortably uses matrices to go beyond two-asset portfolio examples.
* Probability and distributions. A good selection of distributions. But please note, however, the four sampling distributions (normal, student's t, F and chi-square) that are essential in Gujarati (for the FRM candidate) are only briefly listed.
* The best introduction to extreme value theory (EVT) that I've read. I have many texts on EVT, but this is where I would point a new learner.
* Actionable review of maximum likelihood estimation (i.e., accessible examples)
* Linear regression is standard but, to distinguish itself again, the book includes prototypical examples of their application in finance (oh, this is why we do linear regression in finance!)
* Tight intro to numerical methods
* Intro to portfolio theory includes utility theory (refreshingly, with examples)
I can't wait to start Volume II!
I have studied this book cover-to-cover, and I dare to say it is the best book from which to learn or review the math foundations used in quantitative finance (financial econometrics and derivatives pricing). I only have a degree of bachelor of science in computer science, with two years of analysis-lite calculus courses plus a one-semester calculus-based probability class, from the University of Toronto back in 1999, and I was able to understand most of this book. I also have very limited amount of time to study (basically just one half hour each week day on BART ride).
For someone with a similar background and time constraint as mine, Professor Alexander succinctly presents the foundational concepts of differentiation, integration, matrix algebra, multivariate probability, statistical inference, numerical methods, and portfolio theory. I had been searching for and could not find another book that covers so much ground in a single volume. Books like Mathematics for Economists (which I also highly recommend) do cover some of the maths, but do so from the perspectives of economics, not finance. Furthermore, they do not cover probability and statistics.
Contrary to what some other reviewers say, I think the use of Excel in the book is one of its best features. The company where I work uses SAS, S-PLUS, R, Matlab and Gauss, so I do have access to these tools. However, not everyone, especially those who are not working at a financial company, is so fortunate. Even though R is open source, it would add another learning curve on top of what is already a formidable challenge. Excel can be considered as the lowest common denominator, and if an algorithm can be implemented in it, you can bet that it can be ported to any other tool. Professor Alexander's avoidance of VBA is also greatly appreciated, as it would just add another layer of unnecessary complexity.
The only thing I miss from this book is more proofs or pointers to where we can find them. Don't get me wrong, this book is both practical and mathematically rigorous, and contains proofs or derivations for many theorems. However, probably due to the lack of space, a number of theorems are stated but not proved. For example, I would love to see more substantiation on why the t distributions are used for inferences on means and why the F distributions are for variance (section I.3.3.8). The standard I use to measure the clarity and completeness (in terms of proving from first principles) of other math books is Calculus by Professor Michael Spivak and Mathematical Statistics for Economics and Business by Professor Ron Mittelhammer (both of which I highly recommend; I am only half-way through the latter though). Having said that, Professor Alexander's book is probably as complete as anyone can make it with so few pages.
There are a number of gems of distilled insight throughout the book that I have not found elsewhere, such as the difference in notations of price between discrete and continuous times (section I.1.4.1) and the difference between "estimation" and "calibration" of models (p. 201). Professor Alexander's quality of being a great teacher and mentor shines through these examples. I wish I could be her student at the ICMA. In a way, I already am.
In summary, I cannot recommend this book highly enough for anyone who is starting to venture into the world of quantitative finance. I have already bought the rest of the volumes (save for volume IV, which is still unpublished) in the series, and I truly look forward to learning from them.
Congratulations, Professor Alexander, for writing this outstanding text.
I'm a Maple and occasional Mathematica programmer. I found this book to be of limited use, in no small part because of its insistence on using Excel as the instruction coding language.
Who is the book meant for? People in finance who are quants and who have to code surely would want some language that permits intensive use. Sorry but Excel doesn't cut it. Fine for those who use spreadsheets. But the intensive math described in the book seems better suited for another language. Yes you can map 1 language into another (basically it's 1 Turing machine into another). But there's a good reason why different languages co-exist, some are better suited for a given task.
It's confusingly written, with dense manipulations whose purpose is often obscure. The pendantic pedagogy here is very tiresome, after going through several hundred pages of it.
And the book uses Excel to demo the equations?! For serious analysis, providing code examples in Matlab, Mathematica or Maple would have been more useful.
A better alternative to this text would be if you search for the Frank Fabozzi series. He has authored or edited a bunch of financial texts that are far easier and more lucid reads.
Product Details :
Hardcover: 320 pages
Publisher: Wiley; Volume I edition (May 27, 2008)
Language: English
ISBN-10: 0470998008
ISBN-13: 978-0470998007
Product Dimensions: 6.9 x 1 x 9.8 inches
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