Reviews (4)

A incomplete work
It's rather frustrated to see the book with this title only values plain call options. It didn't give a general approach for valuing general payoff securities. The transform formula only works for plain call option, and even this need to use put call parity once to convert the payoff function so that the fundamental solution can apply.

More than just stochastic volatility
Other reviewers discussed the virtues of this book as a first book devoted to option pricing under stochastic volatility. And, indeed, the book provides a detailed exposition of stochastic volatility models. What I wantto add to the other reviews is that this book is more than just aboutstochastic volatility. The book gives a careful exposition of theapplication of the two important mathematical methods to contingent claimvaluation: the method of integral transforms (Fourier and Laplace inparticular) and the method of eigenfunction expansions. Long the core toolsin mathematical physics, these important methods now find more and moreapplications in financial economics. They can be applied to option pricing,interest rate modeling, and, more generally, any problems in economics thatinvolve calculations with diffusion processes. The author clearlydemonstrates how to use these powerful tools for calculations in finance.Researchers working in the area of derivatives pricing, both in academiaand on the Street, will not want to miss this point.

the first book on stochastic volatility models
The Black-Scholes model for the pricing of derivatives whilst very effective is also known to be imperfect. A number of ways of generalizing the model to cope with these imperfections have been developed. One popularmethod is to allow the instantaneous volatility parameter to follow astochastic process. This allows the possibility of observed volatilities inthe market to evolve from day to day and also to produce market type"smiles" that is graphs of volatility against strike which aresmile shaped rather than the horizontal line implied by the Black-Scholesmodel.

In this book, Lewis develops pricing formula for options understochastic volatility models. This is mainly via the use of transformmethods, that is a closed form solution is developed for the Fouriertransform of the price as a function of log of the spot.The actual priceis then obtained via a numerical inverse Fourier transform.

Thestrengths of this book are that it covers an important area that heretoforehas been restricted to research papers and that it provides a large numberof carefulderivations and formulas.

The principal weakness is that theapproach is too formula-based. The reader does not gain many conceptualinsights from the author. Indeed one gains the impressionthat the authoris technically strong but does not have a good conceptual understanding ofthe subject. The author does not really make a case for stochasticvolatility models as opposed to other generalizations of the Black-Scholesmodel.

The book is restricted to vanilla options with no discussion ofhow using astochastic volatility model impacts on the price of exoticoptions.

Reviews (1)

AReview for Programmers, by a Programmer
7.24.99 SJW*****

This is something of a book review, but also a commentary on the Mathematica package. My background is a recent MS in Computer Science.My interest in Mathematica is as a thinking tool forProgrammer/Analysts or R&D Prototypers.

John Gray's book comes with aCD-ROM including the entire text of the book (the book was produced usingMathematica) as well as help files which can easily be integrated into theresourcesof the Mathematica Help Browser.

The book is well laid out(see the Table of Contents at amazon.com) topically, starting with verybasic usage of the math abilities, and the user interface, then moving onto programming styles using Mathematica and methods of representinginformation in Mathematica. (All major commands in the Mathematica packageare searchable, topical resources are available via documentation chapterson that topic, andexplanatory text is hyperlinked in html format.)

Thebook's style is absolutely functional, and is targeted at users who have atleast athreshhold knowledge of modern programming. Much of the materialsomewhat assumes that the reader has read enough using the Help Browswerwith its on-line manual to be able to operate the notebook interface.Examples are given for almost every topic (the examples are executable inMathematica, as the text of the book is in the form of aMathematicanotebook), although the specifics of each example are not necessarilyexplained.

As a programmer, the most amazing revelation of Gray's book isthe degree to which the Mathematica package is programmable. Of course,procedural commands are built in to allow the coding of proceduralalgorithms (these commands have the form of generic pseudocode commands, or"near-C"). But Gray gives examples of programming using functions(recursion is allowed), as well as instructions re o-o and constraint(rule-based) styles of programming. (Note that Mathematica has built inpattern matching notations--especially useful for rule-basedprogramming.)

In short, not only is Mathematica a completely integratedsymbolic/numeric advanced math utility with integrated graphics andstatistical packages, but it also has its own virtual operating system(full file i/o controls), and it allows the user to write rule-basedprograms (such as LISP or Prolog interpreters) which have full access toall of the built in Mathematica abilities, and to custom compiledcomponents which the user has written.

Because all Mathematica'sabilities are integrated, data can easily be displayed graphically,allowing visual debugging of difficult algorithms, or analysis (orreports). Gray provides a few examples of the visual display ofalgorithms.

Reviews (16)

Excellent Practical Tool for Financial Engineers
I found William Shaw's book fascinating when I first bought it back in 1999 and have recently gone back to it for some further insight on some complex problems in finance.
It is a well-structured book that requires a basic understanding of both quantitative finance and Mathematica before you can really get to grips with it BUT having said that the complexity that the author gets to is excellent.
I would recommend this book to anyone in University studying for a Quant-rlated finance Masters or PhD - and anyone practicing in the real world - this should be on your shelf alongisde your copy of Mathematica.

A potentially very good book with a very messy presentation.
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.

Reviews (1)

Reviews (2)

Great Introduction...
Here is a practical comment for the typical economics graduate student: Buy this book if you want to start using Mathematica!

What does a typical economics graduate student need? First, s/he needs to review her/his knowledge of mathematics. Second, s/he needs to learn how to use the tool (math) to solve an economic problem. Cliff J. Huang and Philip S. Crooke's book is helpful in both respects. While they are introducing the basic language of Mathematica they review most of the undergraduate math. And they teach with a hands-on approach--that is, you solve almost every problem using Mathematica.

Mathematica is a great tool for economics graduate students, it helps you out in understanding the basic intuitions behind mathematical concepts--because you do not have to solve complex problems (Mathematica solves them for you), you just have to understand them. Of course, students are advised to consult their professors to choose the right computer software or programming language. Mathematica can do a lot, but some other software might be much more practical for your PhD thesis project...

[Also consider Differential Equations: An Introduction with Mathematica by Clay C. Ross]

Exceptionally valuable contribution to graduate economics
This book covers mathematical methods topics that would ordinarilyconstitute the core of a one semester course at the first year graduatelevel in economics.The book could also be used at the advancedundergraduate level.It is the first book to fully integrate WolframResearch's Mathematica software into a study of mathematical methods foreconomists.The authors' stated objective in this integration is torelieve students, via use of computer software, of the rather tediouscomputations typically associated with mathematics for economistscoursework so that attention can be focused on underlying principles.Tofurther this objective, a Mathematica notebook, MathEcon, comprised offunctions commonly implemented in mathematics for economists coursesaccompanies the book.

The book features fifteen chapters includingcoverage of topics in linear algebra, quadratic forms, vector calculus,functional properties, mathematical programming, and differential anddifference equations.The first two chapters provide an introduction toMathematica and a review of calculus.Chapters are divided into sectionsand subsections and all chapters include exercises at the conclusion ofeach subsection.Many, though not all, of the exercises involve use of theMathematica software.Numerous examples are included in all chapters andthe use of Mathematica to illustrate concepts and problem solving isprevalent throughout the book.In this regard, the numeric, symbolic, and,in particular, graphic capabilites of Mathematica are used extensively toexplain concepts and example problem solutions.

Isbn: 0124649920
Sales Rank: 1045792
Subjects:  1. Computer Bks - Languages / Programming    2. Computer Science    3. Computers    4. Differential Equations    5. Discrete Mathematics    6. Mathematica    7. Mathematica (Computer program    8. Mathematica (Computer program language)    9. Programming Languages - General    10. Science/Mathematics    11. Mathematics / Differential Equations   

Reviews (1)

Isbn: 0387945903
Sales Rank: 2690678
Subjects:  1. Computer Bks - Other Applications    2. Discrete Mathematics    3. Miscellaneous Software    4. Computers / General   

Isbn: 0387946454
Sales Rank: 1334135
Subjects:  1. Computer Bks - Other Applications    2. Discrete Mathematics    3. Mathematics    4. Miscellaneous Software    5. Science/Mathematics    6. Computers / General   

Reviews (1)

AReview for Programmers, by a Programmer
7.24.99 SJW*****

This is something of a book review, but also a commentary on the Mathematica package. My background is a recent MS in Computer Science.My interest in Mathematica is as a thinking tool forProgrammer/Analysts or R&D Prototypers.

John Gray's book comes with aCD-ROM including the entire text of the book (the book was produced usingMathematica) as well as help files which can easily be integrated into theresourcesof the Mathematica Help Browser.

The book is well laid out(see the Table of Contents at amazon.com) topically, starting with verybasic usage of the math abilities, and the user interface, then moving onto programming styles using Mathematica and methods of representinginformation in Mathematica. (All major commands in the Mathematica packageare searchable, topical resources are available via documentation chapterson that topic, andexplanatory text is hyperlinked in html format.)

Thebook's style is absolutely functional, and is targeted at users who have atleast athreshhold knowledge of modern programming. Much of the materialsomewhat assumes that the reader has read enough using the Help Browswerwith its on-line manual to be able to operate the notebook interface.Examples are given for almost every topic (the examples are executable inMathematica, as the text of the book is in the form of aMathematicanotebook), although the specifics of each example are not necessarilyexplained.

As a programmer, the most amazing revelation of Gray's book isthe degree to which the Mathematica package is programmable. Of course,procedural commands are built in to allow the coding of proceduralalgorithms (these commands have the form of generic pseudocode commands, or"near-C"). But Gray gives examples of programming using functions(recursion is allowed), as well as instructions re o-o and constraint(rule-based) styles of programming. (Note that Mathematica has built inpattern matching notations--especially useful for rule-basedprogramming.)

In short, not only is Mathematica a completely integratedsymbolic/numeric advanced math utility with integrated graphics andstatistical packages, but it also has its own virtual operating system(full file i/o controls), and it allows the user to write rule-basedprograms (such as LISP or Prolog interpreters) which have full access toall of the built in Mathematica abilities, and to custom compiledcomponents which the user has written.

Because all Mathematica'sabilities are integrated, data can easily be displayed graphically,allowing visual debugging of difficult algorithms, or analysis (orreports). Gray provides a few examples of the visual display ofalgorithms.

Isbn: 0387942823
Sales Rank: 115184
Subjects:  1. Computer Bks - Languages / Programming    2. Computer Books: General    3. Computer Science    4. Computers    5. Data processing    6. General    7. Mathematica    8. Mathematica (Computer file)    9. Mathematical & Statistical Software    10. Mathematics    11. Programming - General    12. Computers / Computer Science   

Reviews (2)

A computer book by a computer scientist
In my opinion the best book about Mathematica
programming around. Not just a list of rules,
but written from the perspective of a computer
scientist, with reasoning behind each construct.
For the person that wants to know why they are
doing what they are doing, rather than just what
they should be doing.
Amazing that it was ever allowed to go out of
print.
Covers all styles of programming, procedural,
recurrsive and functional.

Reviews (1)