Modelling Financial Derivatives with MATHEMATICA ® [Hardcover]

William T. Shaw (Author)

Book Description

ISBN-10: 052159233X | ISBN-13: 978-0521592338 | Publication Date: January 28, 1999

One of the most important tasks in finance is to find good mathematical models for financial products, in particular derivatives. However, the more realistic the model, the more practitioners face still-unsolved problems in rigorous mathematics and econometrics, in addition to serious numerical difficulties. The idea behind this book is to use Mathematica® to provide a wide range of exact benchmark models against which inexact models can be tested and verified. In so doing, the author is able to explain when models and numerical schemes can be relied on, and when they can't. Benchmarking is also applied to Monte Carlo simulations. Mathematica's graphical and animation capabilities are exploited to show how a model's characteristics can be visualized in two and three dimensions. The models described are all available on an accompanying CD that runs on most Windows, Unix and Macintosh platforms; to be able fully to use the software, Mathematica 3 is required, although certain features are usable with Mathematica 2.2. This product will prove of inestimable worth for financial instrument valuation and hedging, checking existing models and for analyzing derivatives; it can be used for professional or training purposes in financial institutions or universities, and in MBA courses.

Editorial Reviews

Review

"...a book for practitioners...full of practical insights from one with both a good grasp of the theory and much practical experience in the field." Mathematical Reviews

Book Description

The idea behind this work is to use Mathematica® to test financial models. Mathematica's graphical and animation capabilities are exploited to show how a model's characteristics can be visualised in 2 and 3 dimensions. An accompanying CD that runs on most Windows, Unix and Macintosh platforms has the machine readable versions of the models; most features require Mathematica 3, though some only need version 2.2.This product will prove of inestimable worth in financial analysis; it can be used for professional or training purposes in financial institutions or universities, and on MBA courses.

Product Details

• Hardcover: 550 pages
• Publisher: Cambridge University Press (January 28, 1999)
• Language: English
• ISBN-10: 052159233X
• ISBN-13: 978-0521592338
• Product Dimensions: 10 x 7.7 x 1.2 inches
• Shipping Weight: 3 pounds
• Average Customer Review: 3.4 out of 5 stars  See all reviews (15 customer reviews)
• Amazon Best Sellers Rank: #2,495,647 in Books (See Top 100 in Books)

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38 of 39 people found the following review helpful:

2.0 out of 5 stars A complete muddle, October 10, 2000

By 

James Frohnhofer "fijimf" (New York) - See all my reviews
(REAL NAME)   

This review is from: Modelling Financial Derivatives with MATHEMATICA ® (Hardcover)

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.)

31 of 36 people found the following review helpful:

2.0 out of 5 stars Try before you buy, June 11, 1999

By A Customer

This review is from: Modelling Financial Derivatives with MATHEMATICA ® (Hardcover)

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.

11 of 11 people found the following review helpful:

2.0 out of 5 stars What's it for?, February 13, 2001

By 

Brian Boonstra (Chicago, IL USA) - See all my reviews
(REAL NAME)   

This review is from: Modelling Financial Derivatives with MATHEMATICA ® (Hardcover)

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.