Customer Reviews

Modelling Financial Derivatives with MATHEMATICA ®

5 star:		(5)
4 star:		(2)
3 star:		(2)
2 star:		(6)
1 star:		(0)

 

 

In the preface the author sets out four goals which he hopes to accomplish.

The first is to show how Mathematica can be used as a derivatives modelling tool. Technically he does show how Mathematica can be used for derivatives modelling, but with virtually no insight about what makes Mathematica special. The code he writes could trivially be ported to FORTAN, Visual Basic or C. In fact, based on his experience as a practioner, one suspects these models were hastily converted to Mathematica from C. In so doing, Shaw shows that he entirely misses the point of Mathematica.

In Gray's excellent book, "Mastering Mathematica" he proposes a fundamental dictum of Mathematica programming: "Treat mathematical structures as wholes. Never tear them apart and rebuild them again." Yet Shaw does precisely that repeatedly throughout this muddle with his "Mathematica implemenations". Shaw devotes a number of chapters to implementing PDE algorithms in Mathematica with no mention of Mathematica's own PDE solvers. By ignoring them, we are left wondering if Shaw found them inappropriate, inadequate, or just didn't know about them. Shaw devotes half a chapter to comparing the relative speeds different methods for obtaining normally distributed random numbers, while just mentioning the included Mathematica function "NormalDistribution" as just another candidate. While this discussion might be interesting for some, it is irrelevant to his stated purpose. The whole point of Mathematica is to do mathematics, without low level programming, and Shaw just doesn't seem to get it.

His second purpose is to present a complete if concise development of the mathematical approach to the valuation of a large class of derivative securities. He failure here is not as obvious. There are about 20 to 25 well written pages explaing the mathematical background of derivative pricing. But there isn't anything in those pages that isn't covered far more clearly in a dozen other places.

His third purpose is to present a balanced approach to algorithm development including analytical, finite difference, tree and Monte Carlo based solutions. He is successful, but frankly, by this point, who cares?

Fourth he intends to highlight the mathematical pathologies that exist in many derivative modelling problems. In this he is most successful, and one wonders why other authors seem to underweight the importance of this. For this alone, I gave him two stars rather than one.

Finally, given the number of typos and poor typesetting, the price tag of $150 is offensive. You would be far better served to get Wolfram's "The Mathematica Book", and Hull or Wilmott on derivatives (and probably still have some money left over.)

I borrowed this book from the library hoping it would be one of two things: a good book about derivatives or a useful book about programming in Mathematica. It fails as both.

As derivative securities are the apparent "hip thing in finance" every publisher seems to want part of this market. Instead of offering anything of value, there is this mentality of "Wow, here is something new. "Derivatives and xxxx" and they rush to publish. This is where this book fits in, rather like most of the books on C programming.

The first chapter is simply an advertisement for Wolfram's Mathematica. Entirely useless. The second chapter gives you an introduction to Mathematica. Oh boy, it teaches you how to plot a sine curve! It is nothing more than a watered down version of chpt 1 of the mathematica book. The remaining chapters are covered better and in more detail in other books. As far as Mathematica Programming, the author writes "... the use of 'Evaluate' is not strictly necessary; however, it is a good habit to get into using it..." (pg. 154), bad grammar, but more importantly he never gives a good reason as to why 'Evaluate' should be used. But who cares? He showed us how to plot a sine curve.

If you have any type of a marginally sophisticated knowledge of derivative securities this book is an utter bore. It will tell you nothing more than you know already. Really, half the book is just redundant nonsense. Writing the code for a call OR a put in the book is nice. Doing it for both is stupid. Print one and just throw the other on the CD. What does Shaw do? He prints not only both, but also the code for ALL of the Greeks of BOTH calls and puts. Was someone trying to reach a page quota?

The author has a poor command of the written word. There are countless paragraphs that are one sentence long. He refers to himself in both the singular and plural. His programming style is disastrous, the author uses (at least) four different variable names for volatility: the greek letter sigma, sd, v, and sigma (limiting the book's value as a reference text). Also the author switches between conventions in naming functions/variables: there is, i.e., BlackScholesCall[x,z,y...] and done[x,z,y,...], the latter would be better named d1[x,z,y,...] (I am getting at the on-again, off-again use of Caps or '_' and 'done' looks like the English word not d_one).

Finally (and I am nit-picking now), the book is just a printed version of a Mathematica notebook. This means it is hard to read. Displayed equations are not centered and italic offset is not present. Just look at the space between the "d" and the "x" in the "dx". You could fit a truck in-between them. It is very tiresome on the eyes. Anyone use to TeX will get an immediate headache.

In short, be careful with this book. Make sure you preserve the right to return it. Varian's book, "Economic and Financial Modeling..." is better, more interesting, and not nearly as expensive.

I use Mathematica to a certain extent in my own quantitative research. I also teach a class in financial mathematics and programming, currently using MatLab (though that will probably change). I was interested in this book first as a classroom text, and second as a reference text for my work. I bought a copy, but I don't think I'll be finding it particularly useful for either purpose.

The book requires too much background to work well as a textbook. As other reviewers have noted, it is insufficient as a text on its own. If you have another textbook, this one would not add a whole lot of value, since the Mathematica-specific formulas substitute in many places for more traditional pedagogy.

As a reference, the book concentrates too much on topics that are either marginally relevant or better treated elsewhere. For example, there is a long discussion of multiple implied volatilities arising from non-vanilla equity options prices. True enough, but who computes implied vols from exotics?

Much of the book discusses various exotic equity options. As an industry, these are no longer a topic of much research interest, and they are covered in other texts (such as Wilmott's large but mediocre tome, Derivatives). Most firms who need these payoffs have already modeled them. Those who haven't will end up wanting them in C++ or maybe Java anyway, since the licensing and distribution of Mathematica would be impractical for an outfit intending on a heavy expansion of its exotics trading.

As is all too typical in derivatives books, the book includes a latter few sections on interest rates, seemingly as an afterthought (I think Hull is guilty of starting this trend, though his later editions mollify it). The models included are outmoded basics, and so would be useful only for exposition. But there isn't enough of that.

Overall, I'm not sure what uses this book has. Other reviewers have taken issue with the quality of the Mathematica examples. I won't speak to that, but I can say that it failed to live up to my hopes, either as an expository textbook or as a research reference.

The last review (below) made a peculiar point about the manner of treating PDE solutions. I very deliberately wrote low-level code so that people could see exactly how each algorithm performed (e.g. explicit vs CN vs Douglas etc.) This part of the theory is not remotely mature, particularly for the non-smooth data boundary data that arise in derivatives, so that blind use of a high-level PDE solver function is totally inappropriate, and you really have to tear things apart. In contrast the use of built-in functions for analytic solutions make sense, but one has to tear apart numerical solutions for both PDEs and Monte Carlo to see how things work. Perhaps a simpler example will make the point. If you want to just solve a non-linear equation, sure you can use FindRoot, but if you want to understand how solvers work, you have to write lower-level code. The book was trying to make this same point in the context of PDE/Monte Carlo solutions, and Mathematica is an ideal tool for exploring these issues. The treatments of numerical PDEs by most other mainstream authors are generally somewhat naive, though Wilmott has at least made a passing reference to more suitable schemes in his more recent texts. I also do not agree with Gray - better to question and check everything. (Ignore the number of stars I give myself - Amazon does not let you post a comment unless you rate the book!)

I like having Shaw's book around. It definitely contains a large amount of information. Shaw definitely knows how to code in Mathematica, though other reviewers -- who know Mathematica more than I do -- noted that his code is C-like and far from optimal. He also definitely knows a lot about financial derivatives. My problems with the book are that it is far from pedagogical, and more than once I look closely at the details of a proof or an argument, only to find that certain crucial information is missing. For example, his discussion of stochastic calculus is far from complete or introductory -- you cannot learn the subject from that discussion, though the author seems to assume that you can. So this definitely not a textbook. I also believe that I have located strange mistakes. For example, in his MonteCarlo simulation, does Shaw use the normal rather than the log-normal distributions? I found it hard to believe my eyes, but running his code actually gave negative stock prices when the volatility was chosen to be large enough. The author never comments on such details. Finally, the book is too expensive, given that it was produced in whole as a Mathematica notebook.

My comments are confined to the chapters on trees and finite difference methods, because that was my primary interest in buying the book. I'll say one positive thing about this book -- it does touch on many pitfalls of pricing derivatives with numerical methods such as finite differences and trees.

However my chief complaint is with the way the (very interesting and important) contect is presented -- Shaw simply contents himself with showing pages and pages of mathematica code, which is ugly and annoying to read. He doesn't even use indentations or keyword-highlighting to make the Mathematica code easier to read. What an unbelievable four-letter-word mess! Many mathematical concepts are buried within Mathematica code. A much better book would have resulted if he sat down and presented math as math rather than as Mathematica code. Very disappointing work from a writer who clearly seems to have an in-depth knowledge of finite difference methods.

This book assumes you already have a strong mathematical background and in finance as well. And unfortunately this book doesnt cover programming i Mathematica in a good way, but you get an overwiev of what can be done with Mathematica, standard functions and abilities and so on. But this stuff is already covered in a better way in eg. Mathematica Handbook. You get some ideas from this book, but its definitely not worth the price.

This book is commendable to those looking for a quick practitioner's introduction to established numerical techniques in derivatives modelling. It is compehensive enough to get you ready to code your own models immediately, using your own choice of finite difference or Monte Carlo schemes.

This is not to say that there are no analytic solutions presented in this book. Quite the opposite: I found the fact that a good third of the space is taken up by investigations into analytic models somewhat disappointing, as that is perhaps the area where Mathematica gives you the least advantage over other platforms.

The part dealing with finite difference and Monte Carlo schemes is excellent, however. The mathematics of the models is introduced in a very clear and concise fashion, and after this no-nonsense introduction you get straight into coding things up in Mathematica.

Against the background of the high-quality discussion of the issues that do find their way into this book, the number of currently important topics that are lacking treatment is regrettable. I would have particularly liked to see examples of inverse problems, letting Mathematica do the work of calibrating model parameters to more market observables than e.g. just constant stock volatility. Wouldn't we all love to use Mathematica for the calibration, as well as the evaluation and benchmarking of such hotly discussed models like stochastic volatility models or local volatility models? How much time we could save by not having to code all these steps in C++ or worse environments! It seems it would have been a small step for the author to take us that little bit further along, but a large step for the majority of the readership who doesn't share the author's proficiency in the use of Mathematica. Still, if this more advanced level of usage is your aim, the book will at least start you off on the right track.

If you use Mathematica to analyze options and derivatives, this book and the accompanying CD belongs on your bookshelf. The price is somewhat deceptive because the book includes what is essentially a complete set of option and derivative pricing models implemented in Mathematica. Comparable models implemented in C++ or as Excel DLL's would cost several thousand dollars. I particularly recommend using this book and Dr. Shaw's models to benchmark the results from the models you are currently using, especially if you developed them yourself. Dr. Shaw clearly documents many of the implementation flaws of different numerical implementations of derivative models and has provided an extremely useful reference.

This book assumes you already have a strong mathematical background and in finance as well. And unfortunately this book doesnt cover programming i Mathematica in a good way, but you get an overwiev of what can be done with Mathematica, standard functions and abilities and so on. But this stuff is already covered in a better way in eg. Mathematica Handbook. You get some ideas from this book, but its definitely not worth the price.