An Introduction to the Mathematics of Financial Derivatives, Second Edition (Academic Press Advanced Finance)

The exposition may not be as rigourous as many people expect it to be, but that's the whole point of the exercise: to give the reader an introductory and motivated first exposure to risk neutral measures, martingales, stochastic differentiation and integration, Ito's lemma, PDE's, stochastic PDE's, equivalent martingale measures, Girsanov's theorem, and a lot more.

This is definitely the very first book that a non-mathematician student of the subject should read. No doubt about that. I guess the burning question now is: Which book makes a natural second read? Baxter and Rennie? Bjork? Bingham and Kiesel? I think it should be one of these three.


Remarkable Introduction to Serious Math, Serious Finance, and Real-World Applications   June 13, 2006
J.F. (NY, NY)
9 out of 9 found this review helpful

Neftci's book is easily grouped into a large number of texts that provide graduate level (considerable more rigorous than the MBA version) introductions to mathematical finance. Some are written for MBA with want to be exposed to as little math as possible without short changing the financial and valuation aspects and with considerable attention to a broad range of financial products and applications (Hull's classic comes to mind). Others are extremely implementation driven and are more a hybrid of finance and computer programming (Duffy, London, Wilmont). Still others are math books that speak above the heads of almost all practitioners and cover the finance topics poorly (or not at all).

Netfci's book is a rare gem in this field. Excellent coverage of financial topics and fundamentals (Arbitrage Theorem, Forwards Futures, Equity Derivatives, Interest Rate Derivatives), serious graduate level review of financial math and mathematical techniques (Probability, Numeric Processes, Binomial Methods, Stochastic Calculus, Finite Difference, Martingales, Monte Carlo methods), and applications (Bond Pricing, Term Structure Modeling, Exotic Options, Rare Event Modeling).

Best of all, it start assuming very little, builds aggressively, and progresses logically.

The biggest drawbacks are a lack of coverage for credit modeling and credit derivatives, Merton-model and contingent claim models for distressed equity, and more common financial engineering applications (hedging, rebalancing).

It is also remarkable well-written.


Ties everything together   January 7, 2003
19 out of 23 found this review helpful

This book is superb. The author seems to predict all the questions the reader might come up while reading and answers them in footnotes or in the main text. This type of progression lets the reader to clearly understand all the basic materials which are prereqs for other more advanced concepts.

Before this one, I read the books by Hull and Wilmott. Hull's text was very good, but the material seemed rather disjoint. I really couldn't grasp the link between tree methods for pricing options, equivalent martingale measure to price options and lastly Black-Schole's PDE methods. However, Neftci links all these three concepts and shows that they are all equivalent under a few assumptions such as Markov. The book is worth reading for this purpose alone. Also, I found Hull's zero coupon bond pricing formula for different interest rate models a bit mysterious. Neftci first justifies the Feynman-Kac formula and beautifully derives a PDE for pricing bonds for these rate models.

However, because the book is such a hassle-less reading the reader is left scratching his head when it comes to think about problems outside those presented in the text. For example, how can we price path dependent options or fix the error of assuming self-financing portfolio when deriving BS PDE. Also, the last chapter on optimal stopping time is full of errors and not explained well at all. Neftci probably included this chapter for completeness.

There is a relatively minor commitment to reading this book but there is a huge payoff. The book reads like a novel and you are nowhere completely cheated since he mentions where he is doing all the handwaving. It clearly explains stochastic processes and explains concepts such as filtration, mean squared convergence, etc. which should prove fruitful when consulting more rigorous sources on it such as Oksendal, Bjork, etc.

Anyways, don't take my words for it just try it for yourself. I am now reading Musiela and Rutkowski and it's a rather smooth transition from Neftci.

PS: Who cares about mathematical rigor anyways. What stocks really follow geometric brownian motion with constant drifts and volatility, etc. There would be no progress made if we care about such nonsense. What matters is what works not what is most mathematically sound and well-defined.


The Best Beginner's Book on Stochastic Calculus Ever Written   April 6, 2009
Anonymous Coward (USA)
7 out of 7 found this review helpful

This book can be summarized in one sentence:

It is the single most gentle introduction to stochastic calculus ever written.

Seriously. You will NOT find a more gentle introduction to this topic. Neftci took a very difficult topic and wrote a very simple and clear book on the subject material.

This book does not dot the i's and cross the t's the way Shrieve does. It's not the clever tour de force that Baxter and Rennie is. You will not be an expert in stochastic calc after reading it. Not by any stretch of the imagination.

However, you'll have a few things that are more valuable than being an expert at stoch calc:

1. You'll have a gut feeling for what all this stuff means. Ever take a really difficult class and you got A's on all the homeworks and tests, but at the end of the semester you scratch your head and wonder what the heck you just learned? Yes, Shrieve, Øksendal, and a whole bunch of others will make you an expert. But you'll get very little gut feeling understanding from those books. They teach you about calculations, and are very skimpy on the meaning or any kind of intuition. This book is ALL ABOUT intuition and meaning.

2. You'll learn what you need to know. Face it. Stoch calc is a part of all financial engineering programs. But how many quants really use it? For every Peter Carr or Bruno Dupire there are hundreds of quants whose main purpose in life is to calculate cashflow waterfalls on Excel or price a CDS using some company's automated CDS pricing program. For the VAST majority of us, stochastic calculus is mostly for our interviews. We're asked what Girsanov's theorem is. Maybe we're asked to price some weird derivative. Maybe. Most likely we're asked to compute something mindless like the change in some function of a stochastic variable. Unless you're interviewing for some kind of quant R&D position, everything you need to know for your interview is in this book. I promise you.

3. You'll be competent enough to have an intelligent conversation with someone about stochastic calc. You'll be in a better position to read and understand the more advanced books and actually "get it" rather than parrot a bunch of calculations.

I can guarantee you -- the people who don't like this book are either the wrong audience for it and should be reading something more advanced, or they're a bunch pretentious a******s who think that a book's value is proportional to how densely packed it is with arcane equations.

And, no, I don't shy away from nuclear chicken scratching. I have a PhD in theoretical physics. I've done my fair share of reading and writing chicken scratching. I'm not impressed by advanced formalism. It has a proper time and place. I *am* impressed by clarity of thought and exposition, and in this regard, this book is in a universe all its own.

Baxter and Rennie comes close, but their book is subtle and clever. And it doesn't cover the wealth of topics this book covers. I love their book, but this book is ultimately more useful. Think about the difference between Feynman's physics books compared to other beginning texts. To see the real beauty of Feynman's approach, you really need to know the topic.