40 internautes sur 46 ont trouvé ce commentaire utile
Dr. Lee D. Carlson
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This book is a lengthy overview of some modern techniques in financial engineering. If viewed from the standpoint of applications of partial differential equations to finance, then this book is a reasonably complete treatment. The author does spend a great deal of time on the more bread-and-butter topics of financial modeling and less on more specialized topics, as for example weather and energy derivatives, where the use of partial differential equations is of upmost importance. There are of course alternative approaches to financial modeling from the mathematical perspective, such as techniques from the theory of stochastic processes and martingales, but a consideration of such techniques would swell the book to over twice the size, and there are other good books that cover thses approaches in detail.
The author uses Visual Basic and Excel spreadsheets to compute the relevant financial quantities, and given the popularity of spreadsheets in finance, this is appropriate. The numerical solution of partial differential equations is most efficiently done using C (or Fortran) and no doubt the author does recognize this, for he does mention translating existing code in C to Visual Basic.
My only major objection to the book is the lack of exercises, which were a major selling point to me in the author's earlier book on derivatives. Having such exercises is indispensable in understanding results of this nature.
The first few chapters of Volume 1 give an elementary introduction to the theory of derivatives and stochastic calculus. The author does remain concrete in his explanations, and he gives a fairly straightforward derivation of the Black-Scholes equation. This is followed by a very quick discussion of Green's function solutions of the equation and introduction to the Greeks. Generalizations of the Black-Scholes model are discussed later, in the context of dividends, foreign currency, and time-dependent parameters. The author does not give a critical analysis of the Black-Scholes equation in these chapters. This would have been useful to both the practitioner and a newcomer to the field. Also, the Black-Scholes can be derived in many different ways, and it would have been instructive to see some of these alternative derivations. There are derivations of the Black-Scholes equations based on concepts from information theory, and these shed light on the limitations of this equation. All of the concepts in these chapters can be found in the author's earlier book on derivatives. The second half of the first volume is an overview of the mathematical techniques used to deal with path-dependent and "exotic" options. Consultation of the references is mandatory for a complete understanding of the ideas in these chapters, for the author is a little lacking on details. In addition, more discussion is needed on case history validation of the many formulas given in these chapters: are these formulas useful in practice? The author also introduces some new concepts in this volume that are not in the derivatives book, one being stochastic control. Also, the author introduces a similarity reduction technique for partial differential equations that is very much like the techniques used in neutron reactor physics. Physicists-turned-financial-engineers will see the similarity between these two approaches.
The last part of the first volume deals with extending Black-Scholes. The author discusses the problems with Black-Scholes but his treatment is too hurried. A better approach might have been to give (historical) examples of what might happen, from an investment/risk management perspective, if the assumptions of Black-Scholes are followed to the letter. He does give references though for a more in-depth discussion. Volatility surfaces, viz a viz the Fokker-Planck equation, are discussed here, and effectively. Again, the physicist reader will pick up on the dialog immediately. Information-theoretic techniques, via entropy minimization, are used, interestingly. It is refreshing to see in this part that the author gets down to an empirical analysis of some important issues (volatility for example).
The second volume is somewhat more specialized that the first and outlines in the first chapters fixed income products, swaps, and interest rate derivatives. Phase plane analysis is employed in the discussion on multi-factor interest rate modeling. The treatment here is too curt and needs considerable expansion. The theory of stability of fixed points under the influence of noise is non-trivial and requires careful consideration. A departure from the framework of partial differential equations occurs in the discussion of the Heath, Jarrow, and Morton model. Noting that this model is non-Markovian, he introduces Monte Carlo simulation as a technique to calculate the expected present values. He remarks that the simulation time to carry this out is very long. The sluggishness of Monte Carlo simulations in this model and others in financial engineering has motivated many researchers and start-up firms to devise techniques to speed up the simulations. Indeed, a whole industry has grown in recent years offering packages and algorithms to speed up Monte Carlo.
Risk and portfolio management are also discussed in this volume, beginning with modern portfolio theory. The most interesting and well-written part is on asset allocation in continuous time. Energy derivatives, an up-and-coming field are also discussed. The author is un-sure of himself in this chapter, but he does give a general but elementary introduction to the subject. This is an area that needs a lot more investigation and research given its importance.
The last part of the book addresses numerical methods, and there is some source code in Visual Basic. Monte Carlo simulation is discussed again, along with an introduction to low-discrepancy sequences. These sequences have been used extensively in recent years to improve the efficacy of Monte Carlo simulations. The author's treatment is very terse but he does give many references.
The author has done a fine job in these two volumes, and he spices up the reading with a litte humour, which does not detract at all from the seriousness of the topics, but instead makes for more enjoyable reading.
36 internautes sur 44 ont trouvé ce commentaire utile
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I have been an appreciative reader of the previous books by Paul Wilmott, and I eagerly bought this updated edition of Derivatives right away. There was no surprise: this is possibly the most comprehensive book on mathematical finance up to date. Several new chapters have been added, some of them addressing very interesting subjects such as stochastic control (one of my favourites), and many others have been expanded. For instance, American options are explained more thoroughly in this edition. You won't need a PhD in math to read the book: it takes little mathematical knowledge to understand the models to a good level of accuracy (strange as it may sound, the author succeeds in demonstrating it is so), and the derivation of more subtle quantitative subjects is straightforward. Wilmott as usual includes some funny lines throughout the text that make the reading light and enjoyable. The drawing boxes depicting the author himself providing concise advice on what issues to focus on may certainly look childish, yet I think they are of some help to the reader. Actually, I think it's impossible to conceive a topic in derivatives theory (and practice, as the author reminds) not covered in these volumes. Do not expect Paul Wilmott on quantitative finance to provide a useful quick reference for formulas and basic ideas, though. The thick and heavy two volumes are a nightmare to carry around (despite the stylish box that accomodates them) and you won't like to browse through the index jumping from one book to the other. Overall, I think this book is a must for all those interested in financial mathematics. Students and first-timers can not, in my humble opinion, find a better textbook for developing a wide knowledge of mathematical finance, and they will certainly read it cover to cover and will have hard time putting it down. More experienced readers might find the level of exposition, especially in the first chapters, quite introductory, but they certainly will appreciate the broad scope of the book and the unconventional yet very enjoyable style with which the subjects are explained. Moreover, Wilmott is available for answering questions and exchanging ideas and opinions, and I think that's a huge resource, considering how greatly knowledgeable he is. There are only two small drawbacks with this book: the price tag and the ugly suit worn by the author (who, surprisingly enough, seems proud of it) in a picture on the back cover of one of the volumes, but serious Wilmott enthusiasts will happily accept both. As a matter of fact, I'm already looking forward to hear about his next (4 volumes, 2K pages?) release.
20 internautes sur 23 ont trouvé ce commentaire utile
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I own a copy of Wilmott's "Derivatives", which I find to be a useful, if somewhat superficial, reference for a wide variety of financial problems. It was worth buying. In his new opus, Wilmott makes an obvious attempt to copy the style and insight of "The Feynman Lectures on Physics". However, Wilmott falls rather short, and cannot deliver anything beyond what is in his previous books. Forget the boxed set and fancy signature, and stick with the previous book.
20 internautes sur 24 ont trouvé ce commentaire utile
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The theory of derivatives pricing is the observation by Black and Scholes that the randomness in the value of an option can be balanced by the randomness of the underlying stock. This leads to a partial differential equation for the price of the option known as the Black-Scholes equation. Following on from this, mathematical finance has developed into a burgeoning field. The PDE approach has however been largely superceded by the more advanced martingale-based risk-neutral evaluation approach.
This book is an extended edition of Wilmott's previous book Derivatives and suffers from similar defects. It is a good basic introduction to the PDE approach to pricing but is limited in scope and viewpoint. Trees, risk-neutral pricing and martingales barely rate a mention. Every problem is fitted into the PDE approach whether it makes sense or not.
If you want to spend a lot of money learning Wilmott's view on finance then this is the book for you. But if you want a good overview of modern financial techniques then save your pennies.
37 internautes sur 47 ont trouvé ce commentaire utile
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Who should buy this book? The real question is who shouldn't buy this book. For the Phd Quant this book is a tour de force in how to explain technical topics clearly and concisely. For the newbie, this is simply the lowest barrier to entry available.
Interestingly, QF does not "replace" a bookshelf of quant books -- rather it nicely compliments many that you're likely to have such as Taleb, Neftci etc. As sales of QF increase, it is likely that readers will be less likely to buy a derivatives book that is over their head.
Volume 1 covers 37 chapters of the equities/currency derivatives world, While Volume 2 covers the Fixed Income World, Risk Measurement , Miscellaneous Topics and Numerical Methods.
Chapter 10 has an excellent and all too rare discussion of Probability Density Functions and First Exit Times, whilst Chapter 14 has an outstanding Trading Game invented by one of Paul Wilmott's former students.
Chapters 16 through 21 cover the Path Dependent world while the balance of the chapters cover extensions to Black Scholes.
Its in these sections that Wilmott delivers some surprising thoughts and insights into Stochastic Volatility Surfaces that are currently the rage.
Throughout both volumes I continue to be astonished at how clear, concise and effective his explanations are. The icons are not annoying at all -- rather I found myself skimming the icons to find out what was required to be committed to memory in each section versus what was background.
As obvious as it sounds, a glaring weakness in Derivatives texts is the inability of authors to elucidate what must be memorized as rote for the student to make further progress. Paul's easy to follow icons lay out a precise plan of study.
I can't say enough about what a leap this is over competing texts.
In Volume 2, Chapters 38 through 50 cover models that Wilmott likes as well as ones that he doesn't [again, a rather novel approach]
Some surprises in Chapters 51 and 52 are an excellent overview of Portfolio Management and a survey of Robert Merton's Asset Allocation in Continuous Time.
Sprinkle in outstanding chapters on Derivatives Fiascos, Real Options, Energy Derivatives and 5 chapters on Numerical Methods and an astonishing survey of Quantitative Finance is complete.
Throughout the books Paul's practical use of Term Sheets and quick and dirty VB code and spreadsheet tricks [you just have to see his Excel shortcut for approximating the Normal distribution] leave the reader constantly wanting to rev ahead.
To round out a tremendous effort, Wilmott also pays homage to authors that he's found helpful and he's generous with suggestions on further reading. This builds sorely needed confidence when attempting new material.
The comparison with Richard Feynman is apt but misses an important detail...Feynman was not noted for turning out hordes of talented understudies. Paul Wilmott has turned out enough talented graduate students that maybe he will be a bona fide cult leader someday.