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Books - Business & Investing - Finance - Finance & Investing - Essential Options and Derivatives

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Options, Futures, and Other Derivatives (4th Edition)
by John C. Hull
Average Customer Review: 4.5 out of 5 stars
Hardcover (15 January, 2000)
list price: $125.00
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Reviews (45)

4-0 out of 5 stars A good first step into the world of Quantitative Finance
The author has written a nice, lively elementary text on mathematical finance. This book can serve as a excellent launching point into the topic. For the next step in the reader's development, I recommend the very good intermediate level treatment by Bjork in "Arbitrage Theory in Continuous Time" 2nd edition. As a capstone for advanced study, I recommend the advanced treatment of Musiela and Rutkowski's "Martingale Methods in Financial Modeling.

Hull starts out his 5th edition with several chapters on the basics of the derivative contracts in his study. The contracts introduced are forward and futures contracts, interest rate swaps, and equity options. The basic definitions of each contingency contract is given, as well as characteristics of the markets where these contracts trade. Some basic trading strategies are also studied.

The study of the option pricing model problem begins in earnest in Chapter 10. The section on one-step binomial tree model leads to a very intuitive description of risk-neutral valuation.

Chapter 11 introduces continuous time stochastic processes in a very intuitive setting. To avoid the hard-core Ito calculus, the author motivates the stochastic differential by considering difference equations. This is a nice technique and makes the material accessible to the beginner. The next highlight is a statement of Ito's lemma. This is not given in full generality, but only stated precisely as needed for Black-Scholes calculations. The appendix gives an intuitive motivation for Ito's lemma based on the multi-dimensional Taylor's formula.
This is a nice illustration as Taylor's formula is indeed a component of the formal semi-martingale based proof of Ito's rule. See for example Oksendal, "Stochastic Differential Equations" Chapter 4, or Karatzas & Shreve "Brownian Motion and Stochastic Calculus, Chapter 3.

Chapter 12 is devoted to the Black-Scholes-Merton theory of option pricing. The famous Black-Scholes PDE is derived via Ito's rule and application of a delta hedge. The author doesn't directly solve this PDE (via the standard application of the Feyman-Kac formula). Instead a nice proof of the option pricing formula is established in the appendix based on a simple log-normal distribution argument.

Chapter 13 discusses option pricing in for other contingency contracts. In Chapter 14, we return to equity options by studying the Greek letters. The reader discovers the Greek letters can be thought of as coefficients of the Black-Scholes PDE and learns some elementary hedging techniques.

Chapter 15 discusses implied volatility and volatility smiles. It is here that the astute reader gets his first indication that the Black-Scholes theory for option pricing may not be as robust or "true to market" as the reader may have been lead to believe. (The folks at Long-Term Capital Management learned this hard lesson rather publicly.)

A survey of topics of interest follows in the next handful of chapters. The material on value at risk, the GARCH volatility model and exotic options is somewhat superficial. The careless reader will come away feeling he knows quite a bit more than he really does.

Martingale theory is touched on in 21 and the Girsanov Theorem is alluded to, but these topics are really too complex and require too many prerequisites for proper treatment in the context. A general multi-variate version of Ito's Rule is stated in the appendix of this chapter.

The next section of the book deals with term-structure models and their applications. One-factor models are discussed along with the various limitations of each of these models. This gives a nice historical treatment. The Heath-Jarrow-Morton and Libor Market Model k-factor term-structure frameworks are introduced. Without the supporting martingale theory, the analysis of these models presented here is very limited.

The last several chapters of the text are very survey-like and breezily touch on topics such as credit risk, credit derivatives and energy derivatives. There isn't a lot of theory in these chapters at all, but at least the reader is made aware of the existence of these kinds of contingencies.

The book wraps up with a cautionary chapter in the form of lessons learned. The unwary reader might see all of the derivative-related train wrecks and say to himself "well, that won't be me". The problem is that it really might be you if you truly (and foolishly) still believe the equity prices always follow geometric Brownian motion. See Lo & MacKinlay "A Non-Random Walk Down Wall Street" for an excellent exposition into the limitations of the basic assumptions underpinning the Black-Scholes-Merton theory.

If nothing else, Hull's last chapter should convince you that maybe this isn't the only book you'll ever want to read in your study of mathematical finance.

5-0 out of 5 stars The bible of derivatives
As the title of this review indicates, this is _the_ book out of many for financial derivatives. It is by no means the only thing you'll need, but it is a great book for a solid foundation in the subject. In short, this book should adorn every finance dork's library.


4-0 out of 5 stars A must-have on your shelf
Both academics and financial practitioners (particularly those who are involved in derivatives) must have a copy on their shelf. It serves as a useful reference to refresh any fading memory since it is quite comprehensive and covers practically the whole spectrum of derivatives.

For undergraduates, there is another version entitled "Fundamentals of Futures and Options Markets" which is highly regarded the standard text for any derivatives course ! ... Read more

Isbn: 0130224448
Sales Rank: 55148
Subjects:  1. Business & Economics    2. Business / Economics / Finance    3. Business/Economics    4. Derivative securities    5. Finance    6. Futures    7. Futures And Options Trading    8. Investments & Securities - Futures    9. Investments & Securities - General    10. Investments & Securities - Options    11. Stock options   

Paul Wilmott on Quantitative Finance, 2 Volume Set
by PaulWilmott
Average Customer Review: 3.5 out of 5 stars
Hardcover (15 January, 2000)
list price: $240.00 -- our price: $151.20
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Reviews (28)

1-0 out of 5 stars Insufficient
This is not as good as Wilmott's earlier work, and even that could have benefited from better definition of terms.Wilmott needs to brush up on the latest techniques and talk to some practitioners to learn how to apply math to real world examples.It seems there is a lack of depth of understanding evidenced by the writing.The sections of self-expose are an embarrassment.

1-0 out of 5 stars Old Material
This is recycled Wilmott, but not even as good as earlier work.His first book was better, probably because his co-authors talked some sense into him.His personal anecdotes demonstrate a low emotional IQ.It is as if Wilmott thinks that if readers agree with the finance they must agree with his incessant and juvenile self-regard.My reaction to the inappropriate self-expose was: "Who cares?Get some friends, they might help on the financial aspects of this book".

Wilmott's financial IQ is only average, if this book is to be the evidence.It seems Wilmott isn't up on the latest techniques, or can't be bothered to research them.Stochastic calculus for example.Lack of real world practical examples demonstrates lack of knowledge of how financial instruments work in practice.

5-0 out of 5 stars The first resource
I own 'most' of the standard texts, oddly enough, this was one of my most recent purchases. Now, whenenver I need to find out about some concept I am unfamiliar with, or brush up on something, this is the first reference. Very often the other books don't get a look in.
Luckily I work from home. They aren't the sort of books you would take home from the office for bedtime reading, unless you did weightlifting as a hobby.
Pity the martingale approach is missing. Ignore the ridiculous comment by another reviewer who dismisses the martingale approach as useless. The approach is hard, that's all. It would be great to see it boiled down in further volumes. ... Read more

Isbn: 0471874388
Sales Rank: 127051
Subjects:  1. Accounting - General    2. Business & Economics    3. Business / Economics / Finance    4. Business/Economics    5. Derivative securities    6. Finance    7. General    8. Investment Finance    9. Investments & Securities - Futures    10. Mathematical models    11. Options (Finance)    12. Prices    13. Business & Economics / Finance    14. Investment & securities   


Introduction to the Mathematics of Financial Derivatives
by Salih N. Neftci
Average Customer Review: 4.0 out of 5 stars
Hardcover (April, 2000)
list price: $71.95 -- our price: $71.95
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Reviews (50)

5-0 out of 5 stars Extraordinarily clear and intuitive
I suggest all to hedge your risk of ignorance by taking a long position in this book immediately!

2-0 out of 5 stars A good first draft not a useful text
I used this text for a graduate course on financial derivatives in an applied mathematics program. The text generally made a good selection of the topics covered, but often key insights and proofs were missing. There were few useful examples and the end-of-chapter exercises were both too few in number and were not well thought out.The material could have been better organized and less meandering. A more compact and rigorous theoretical presentation surrounded and amplified by lots of good examples--including some involving numerical techniques--would have been both deeper and more accessible to students. As an instructor, I found the text was usable, but required me to add a great deal of my own material for the students. Finally, the index is just about useless, making it difficult to use this work as a reference.

4-0 out of 5 stars Good Book
I've read Hull, Wilmott and Baxter books but definitely like this book better - particularly for entry (but not easy) level derivative math. Can't say much since English is not my first language. But if you want to learn about Derivative Math and don't have strong background in Math (I'm a Porfolio Manager and have pretty good background in Calculus, Differential Equation, Econometrics) this book is certainly worth considering.I give 4 stars due to the lack of practice problems. ... Read more

Isbn: 0125153929
Sales Rank: 111161
Subjects:  1. Accounting - General    2. Applied    3. Banks & Banking    4. Business & Economics    5. Business/Economics    6. Derivative securities    7. Finance    8. Investment Finance    9. Investments & Securities - General    10. Mathematical Economics    11. Mathematics    12. Applied Economics    13. Applied Mathematics    14. Business & Economics / Finance    15. Econometrics    16. Microeconomics   


The Econometrics of Financial Markets
by John Y. Campbell, Andrew W. Lo, A. Craig MacKinlay, Andrew Y. Lo, Archie Craig MacKinlay
Average Customer Review: 4.0 out of 5 stars
Hardcover (09 December, 1996)
list price: $95.00 -- our price: $71.44
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Reviews (12)

3-0 out of 5 stars Very Good but Not Enough
I just used this book in my master in finance course and think its very good but a bit outdated and incomplete. I was able to benefit from it, but only because of my previous strong finance, econometrics and computing knowledge. Without any of my skills i would be surely lost. The sad part is i cant remember another book filling its niche. Maybe only John Cochrane "Asset Pricing" overlaps well in some subjects.

The book outline the econometrics of major finance issues, but doesnt give detailed descriptions of main results. As an example, the Maximum likelihood formulas for multifactor asset pricing models are simply shown, but they dont explain how they got there (the likelihood function), so additional effort is needed if one wants to modify something - [A Critic : If you need to work on the econometrics of something yourself you dont need to buy the book, just learn finance and econometrics and put it together yourself !!]

The book maybe useful as a reference on many subjects, but to actually implement the models (as a practictioner or analyst) you will most likely need additional knowledge/books on a given subject. They also dont show any kind of algorithms/computing techniques or codes to do implement it, so you must be skilled enough at computing to crack it.

As an improving suggestion, the authors should reduce the number of chapters/subjects, completing it with more detailed formulas and computer codes/guides to actual implementation.

1-0 out of 5 stars Spend your money on something better
This book seems to have written to cash in on the fame of the authors and the stampede in academia and industry towards financial econometrics.

The book already assumes you are proficentin basic and advanced econometrics, derivatives pricing, fixed income, microstructure, neural networks etc. If you already familiar with those fields, why do you need this book? For example, Chapter 10 on Fixed Income Securities covers a grand total of 28 pages beginning with "Basic Concepts" and ending with "Yield Spreads and Interest Rate forecasts".Meanwhile there are whole tomes devoted to every one of those sections in Chapter 10. Nonparameteric Estimation merits a grand total of 9 pages and Neural networks merits 7 pages in Chapter 12.

The chapter on Microstructure, virtue of the book being published in 1997 is thoroughly dated. Even for its 1997 publication the chapter is thoroughly lacking. It is neither a survey nor a exposition of theory or practial uses of microstructure theory. Today there are excellent theoretical and practical books devoted to every topic covered in this book.

Save your money for one of those.

5-0 out of 5 stars Superior Treatment of Econometrics
Campbell, et. al. have put together the defining book in econometrics.The deep and well thought out explanations of econometrics lend themselves to theories and applications for the behavior of even the most elusive driving forces.I even found a framework for valuing credit derivatives supplementing the descriptions of value in "Credit Derivatives" by Tavakoli.

I admit that readers with no background in econometrics may wish to start with lighter reading, but this book is a must, and worth the effort. ... Read more

Isbn: 0691043019
Sales Rank: 113805
Subjects:  1. Business & Economics    2. Business / Economics / Finance    3. Business/Economics    4. Capital market    5. Econometric models    6. Finance    7. Financial Markets    8. Investments & Securities - General    9. Mathematical Economics    10. Business & Economics / Investments & Securities    11. Economics   


Dynamic Asset Pricing Theory. Second edition
by Darrell Duffie
Average Customer Review: 4.5 out of 5 stars
Hardcover (22 January, 1996)
list price: $59.50
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Reviews (6)

5-0 out of 5 stars Finance for economists
This book provides the most elegant and coherent synthesis of finance theory, in a complete markets and frictionless settings.

For the reader interested in the theoretical foundations of modern financial models, this book has three main advantages over many of its competitors:

- It clearly shows the link between modern finance theory and the 40-year old Arrow-Debreu model. As this book will make clear, financial assets can be viewed as "bundles" of Arrow-Debreu contingent goods, and pricing kernels are simply extensions of Arrow-Debreu contingent state prices.

- It bridges the gap between arbitrage models on one hand, and models based on consumption, optimization/dynamic programming and general equilibrium on the other hand. Absence of arbitrage guarantees the existence of a stochastic discount factor, or pricing kernel. Optimality implies that the stochastic discount factor must be equal to the investors' intertemporal marginal rate of substitution.

- It provides a unified treatment of discrete-time and continuous-time models. Many finance textbooks focus on the mathematic tools and emphasize the difference between continuous-time and discrete-time tools--usually at the expense of the economics underlying both types of models. In contrast Duffie's book emphasizes the conceptual unity between continuous-time and discrete-time asset pricing.

This book was written more for students and academics than for pratictioners. It is not a reference or a recipe book for traders and programmers. Several chapters are devoted to general-equilibrium models that pratictioners are not likely to find useful. However, the essentials of derivative asset pricing and the term structure are also covered. The latest edition even includes a chapter on corporate finance.

Finally, this book is pretty much self-contained. All the graduate-level math results used in the proofs are presented either in the main body of the book, or in appendices.

5-0 out of 5 stars Demanding but rewarding!
First of all, this book is for people with advanced mathematical preparation. Courses in functional analysis, measure theory, stochastic calculus and vector space optimization are in my opinion required for a deep understanding of the material in the book. Fortunately, the appendices are very good and provide many things that can help someone to follow the book.
In the first four chapters the writer develops the discrete-time theory,in order to provide a better understanding of the underlying ideas which remain the same in the next chapters which deal with the continuous-time setting.
Although the book needs a lot of effort from the reader, it is unique in that can help you see beyond the mathematics. In other words it USES the mathematics and it isn't just a layout of theorems and proofs.
Of course it can't be compared with books like Hull as it isn't accessible to everyone. But someone with the mathematical preparation , who has read Hull , should buy this book and he will never regret it.

4-0 out of 5 stars Pricing for Traditional Products
This is a good book for traditional products, but doesn't stay ahead of the curve for people who need to keep up with current capital markets products.Still, the basic tools are there for those who already understand the products.

In the exponentially growing credit derivatives market, the market appears very inefficient.Information on documentation and pricing is not at all transparent, and information requires time and work to obtain.This was a nothing market 6 years ago, was a $2 trillion market in 2002, and is on a steep exponential growth curve just in credit default swaps.In a paradigm shift, it has become a very important product in a very short time, and the market in these products is inefficient. For product and performance descriptions I highly recommend Tavakoli's book: "Credit Derivatives" Second Edition. ... Read more

Isbn: 0691021252
Sales Rank: 684192
Subjects:  1. Business / Economics / Finance    2. Business/Economics    3. Capital assets pricing model    4. Investments & Securities - General    5. Portfolio Management    6. Uncertainty   

Continuous-Time Finance
by Robert C. Merton
Average Customer Review: 5.0 out of 5 stars
Paperback (01 June, 1992)
list price: $54.95 -- our price: $54.95
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Reviews (2)

5-0 out of 5 stars Collection of past papers
This book is a collection of thier(most of the parts are Merton's) papers written during the past 25 years. The papers are little bit changed so as to be cross-referenced through the book. Also You can find some comments inthe book for the recent literatures. As you know, Dr. Merton introducedcontinuous-time approaches into the finance. This book deals with basicmathematics for the continuous time finance, portfolio selection, optionpricing, and theory of intertemporal equilibrium. The value of this book isgreater than that of papers copied separately in the library. Also it is agreat pleasure to see how his theory has been evolved through the book.

5-0 out of 5 stars The bible of continuous time approach to financial theory
I think the Nobel Prize was not enough to thank Professor Merton for his thought. The absolute and necessary book to approach continuous time Finance. ... Read more

Isbn: 0631185089
Sales Rank: 176538
Subjects:  1. Business / Economics / Finance    2. Business/Economics    3. Finance   


Financial Calculus : An Introduction to Derivative Pricing
by Martin Baxter, Andrew Rennie
Average Customer Review: 4.0 out of 5 stars
Hardcover (19 September, 1996)
list price: $66.10 -- our price: $44.24
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Reviews (24)

5-0 out of 5 stars A gem of a book
This small textbook is a hard find in the finance world. The authors have managed to clearly explain a topic that is very difficult and unclear to begin with. It would be nice to see this book expanded into a larger text with practice problems, solution sets, and discourse on relevant research and current journal articles. Nonetheless, I thoroughly recommend this book to students and practitioners of finance alike.


5-0 out of 5 stars A nice place to start
This is a good place to start if you have a good grasp of calculus and probability (just undergrad level-no measure theory or SDE needed). I am using it as a main text for a class and the book is very compact and precise as the same time it covers the main battle ground of the field of financial mathematics.

My training is math and when I need the financial applications, I support it with John Hull's bible. As a math person, I get tiered of reading the pages and pages of long stories in Hull'sbook which can be summarized by a couple of equations with brief description. Hence, if you are like me who can understand (short) stories equipped with mathematical symbols, I definitely recommend you start here.

4-0 out of 5 stars Compact, accessible yet rigorous introduction.
This text is a useful introduction to derivatives pricing. The examples and exercises are well-thought out and relevant, but I took off a star because there weren't more of them. One of the authors' stated goals was to bring the text's readers up to a level of rigor that would enable them to model new financial products for which "off the shelf" tools were not available. They succeeded admirably.

This ought not to be the only such book in your library, but if you need a quick but still rigorous introduction or if you're a student struggling with a less than idea class text, this work is invaluable. ... Read more

Isbn: 0521552893
Sales Rank: 18655
Subjects:  1. Calculus    2. Derivative securities    3. Economics - General    4. Investment Finance    5. Mathematics    6. Prices    7. Probability & Statistics - General    8. Science/Mathematics    9. Finance    10. Mathematics / Statistics    11. Probability & statistics   


Black Scholes and Beyond: Option Pricing Models
by Neil A. Chriss
Average Customer Review: 4.5 out of 5 stars
Hardcover (01 September, 1996)
list price: $65.00 -- our price: $40.95
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Reviews (9)

5-0 out of 5 stars Recommneded for traders with advanced math skills
This book isn't about teaching you how to place an option trade and profit. Instead, it's about the mathematics behind option pricing model. I am a beginner in options trading and was looking for answers on how options get priced and what parameters affect the price. To be more precise, I was carious to know how the formula looks like. I learned from the book important things like Delta, Gamma, Vega parameters and their impact on pricing options.

5-0 out of 5 stars Logical progression of ideas in a lucid style
I picked up this book as additional reading for an actuarial exam on investments, in hopes of getting a better and more intuitive understanding of the Black-Scholes Formula.This book develops ideas in a clear, natural, intuitive sequence.I particularly commend the author for a lucid and agreeable style.I was expecting a book on this kind of subject to be dry and heavy-going, but instead what I found was a very good teacher guiding me through the subject.It should be mentioned that the development of the formula entirely from scratch is not in this book, as that would basically require stochastic calculus or other techniques beyond the scope of the book.Even so, he does explain the rationale behind the formula as well as related concepts such as hedging away risk and self-financing strategies.He gives the appropriate versions of the Black-Scholes Formula for stocks with continuous or lumpy dividends and, of course, talks about put-call parity for European options.There is excellent coverage of The Greeks (delta, gamma, vega, etc.) along with numerous graphs.A nice surprise was the inclusion of some approximation formulas for the cumulative normal distribution that can be calculated easily with a spreadsheet or calculator.Finally, he has very good coverage on binomial trees, of both the classic "Cox-Ross-Rubinstein" and the "flexible" varieties.I have to admit that I have read only through Ch. 7 so far (which is approx. 2/3 of the book), but I will probably keep going because it is so good.

5-0 out of 5 stars Outstanding and Easy to Follow
Great book for practitioners in finance without cumbersome math formula! ... Read more

Isbn: 0786310251
Sales Rank: 152494
Subjects:  1. Business & Economics    2. Business / Economics / Finance    3. Business/Economics    4. Finance    5. Futures And Options Trading    6. Investments & Securities - Options    7. Mathematical models    8. Options (Finance)    9. Prices    10. Business & Economics / Investments & Securities   


The Complete Guide to Option Pricing Formulas
by Espen Gaardner Haug
Average Customer Review: 4.0 out of 5 stars
Hardcover (01 September, 1997)
list price: $55.00 -- our price: $34.65
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Reviews (24)

2-0 out of 5 stars Nice idea, but MANY errors
This book is the "standard" for providing straightforward code demonstrating various options pricing techniques, and perhaps deservedly so -- after all, it really doesn't have too many competitors in that niche. However, even in the course of the fairly straightforward applications I've had for this book (mostly simple equity Cox-Ross and Black-Scholes modeling), I've been shocked by the number of blatant mathematical errors (in the formulas for rho with distinct carry and risk-free rates, for instance). Clearly, the author and editors didn't bother to spend much time verifying that the formulas they cite are actually correct. (I'm actually shocked to see a fellow reviewer praise the "proofreading" -- I'm guessing he or she never actually had to use any of the formulas in this book!)

Bottom line -- if you're looking for a handy, compact reference of option pricing formulas, this is probably what you'll end up with. But be careful. It is SO frustrating to spend hours trying to figure out where you made a mistake in implementing one of these models, only to learn that you DIDN'T make a mistake -- the mistake was in your source. Consider yourself warned...

1-0 out of 5 stars Numerous technical mistakes
I have reviewed many of the formulas in several sections of this book and have found a number of mistakes.As a result, I can trust no formula from the book without reviewing the literature or some other source.

The author does not use consistent terminology throughout the book.Rather, the terminology of the original journal article is used for each pricing model.This makes referring to the articles convenient, but then you don't need the book if you're going to the source...

I have used few of the computer programs offered, but the ones that I have used have had terrible inefficiencies.For example, a bisectional iterative search was used, which is very simple to write but is also very inefficient.There are many other simple and more efficient alternatives.

5-0 out of 5 stars THE Reference Manual
Fantastic reference manual for the most basic to unusual options.Well organized making it easy to find what you're looking for.If you're looking for derivations of models, you've got the wrong book.If you're looking for formulaes and perhaps even spreadsheets, this is the book for you.

I know of no other book as comprehensive as this book.I don't know if there will be a revised edition, but if there is, I will certainly buy it since this is, in my mind, the definitive reference manual. ... Read more

Isbn: 0786312408
Sales Rank: 25168
Subjects:  1. Business & Economics    2. Business / Economics / Finance    3. Business/Economics    4. Finance    5. Futures And Options Trading    6. Investments & Securities - General    7. Investments & Securities - Options    8. Mathematical models    9. Options (Finance)    10. Prices    11. Software    12. Business & Economics / Investments & Securities   


The Mathematics of Financial Derivatives : A Student Introduction
by Paul Wilmott, Sam Howison, Jeff Dewynne
Average Customer Review: 3.5 out of 5 stars
Paperback (29 September, 1995)
list price: $42.99 -- our price: $42.99
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Reviews (16)

1-0 out of 5 stars waste of time
This book is very bad, lacks almost everything you can think of, but if you don't know any better you probably won't care. It certainly needs to be supplemented by a respectable book if you want to learn derivatives (c.f. Hull's textbook, for example), and on the other hand, the math isn't rigorous at all, so you'll need a book on stochastic calculus (e.g. Michael Steele's, actually there are tons of better books out there, it's not hard to find better).

4-0 out of 5 stars Only one snag
There is no portfolio analysis which ,I think, is basic to any book in financial math.

1-0 out of 5 stars Read Hull Instead
It seems the examples in this book are clones of those found in Hull.Odd, since the author seems to want to use more sophisticate math.Since the author can't explain calculus or properly define terms, there is doubt there is even that basic understanding.Pass on this and buy Hull instead for better clarity and better examples. ... Read more

Isbn: 0521497892
Sales Rank: 205436
Subjects:  1. Business / Economics / Finance    2. Derivative securities    3. Investments & Securities - Options    4. Mathematical models    5. Mathematics    6. Options (Finance)    7. Prices    8. Probability & Statistics - General    9. Reference    10. Science/Mathematics    11. Investment & securities    12. Mathematical modelling    13. Mathematics / Statistics   


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