Customer Reviews

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

5 star:		(40)
4 star:		(15)
3 star:		(3)
2 star:		(7)
1 star:		(7)

 

 

I used this book to teach a Financial Mathematics course, and found its explanations to be generally clear and good. However, part of the reason the text seems so clear is that it doesn't explain much of what's really going on. It covers the right material, but not really in such a way that the reader can then go on to apply the knowledge gained.This is evidenced by the complete (and almost unforgiveable) lack of exercises in the book. It is very easy to feel you understand this sort of material, only to be completely lost when you actually have to solve a problem. Neftci will not help in this regard. I understand that it is difficult to create good exercises, but their absence almost makes me wonder if Neftci realized he was not explaining things in enough detail to let the student actually work with the knowledge. Exercises are the only way to really learn this subject.A basic problem with all these texts is that, try as they might, they cannot impart true understanding unless the student can grasp real analysis at, say, an undergraduate level typically reached by students at a good engineering school. This text tries to avoid the problem by failing to mention any of the analysis...that's not likely to work.

Students of derivative pricing techniques are often in a dilemma: Coming from their MBA or undergrad course, they have just build a "brealy-myers" type of intuition on options. Moving towards Hull then allows a deeper understanding. But any serious (eg PhD, Wall Street Analyst) student of derivatives needs to undertstand the math behind modern derivatives pricing. Essentially, this research divides into two streams: Solving Partial differential equations and developing equivalent Martingales. Without a rigorous pre-education (Maths, Physics), most students fail to understand (let alone learn to use) these methods. Nefci is the only book that does not assume lots of prior knowledge, as compared to Merton (1992) or Duffie (who is so bold to write "for mathematical preparation little beyong undergraduate analysis...is assumed" -ask PhD Students how easy this book reads! The answer is its tough!!). In Short, Neftci's book is a true blessing for all "normal" people. Can't wait to get the second edition!

While most MBAs are already separated into those strong in math who gravitate towards the mathematically more intense areas such as finance and those who head towards areas less mathematically intense such as marketing and organizational behavior, there are many of us who know we need to strengthen our mathematical understanding. For us, this book by Prof. Neftci is a gift!

Now, I am NOT bashing marketing and organizational behavior. In fact, math can be used to great advantage in those fields, but you do find many who feel very uncomfortable with much beyond algebra and that is ok, too. And it is very possible to work in finance without understanding the math behind the tools and principles taught in the basic courses. However, if you want to go deeper than the basic courses this book can be a great next step.

The truly mathematical seem to feel that this book doesn't go far enough and that may be true if you want to get to the very bottom of the subjects reviewed here. If you think of this book as an intermediate step that gives you more than the simple treatment you get in most MBA courses and not as intense as you would get in "Continuous Stochastic Calculus with Applications to Finance" and that is what you want then this book is for you (and for me).

Plus there is a nice bibliography that can help you dive even deeper.

Neftci makes a valiant and serious attempt at explaining stochastic calculus and related mathematics of financial derivatives to the non-expert. I think he succeeds.

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.

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.

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.

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.

Neftci does a good job in introducing the mathematics of financial derivatives to its readers. This book is ideal for MBA level quant finance knowledge. It does not go into rigorous mathematical depth but does a smart job of discussing the physics behind the principles of pricing derivative securities. The best part about this book is its parallel handling of PDE approach and the equivalent martingale measure. There is sufficient coverage for introductory level fixed income pricing mechanisms. The book does a good job in the end by converging the ideas of the two pricing methods. This gives a lot of clarity in the science behind such derivative contracts.

Although the theory is covered clearly the problems are not correlated with the chapter contents. Do not get disheartened if you are not able to ace the problems. Rather use this book to build the base and clear the concepts.

This book was an enjoyable read (as maths texts go). It finds a nice balance between rigour and ease of understanding. Each idea is introduced slowly, which may frustrate a more advanced reader (I found it annoying that it kept hinting at the Ito integral, yet left the formal definition until 9 chapters in ). That apart, this is a great book for getting up to speed on stochastic calculus in a Finance setting. What is even better (and something I feel that some of the other reviews have failed to mention) is that at the end of each chapter it tells you where to look for more information. HENCE if the material is not rigorous enough, it at least tells you where to look for a more formal treatment. Worth the money.

The best introduction to Stochastic Calculus.
As a quant finance tutor on the 7city CQF course I have consistently (and without hesitation) recommended this text to course delegates and university students.