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Arbitrage Theory in Continuous Time [Hardcover]

Tomas Björk
4.7 out of 5 stars  See all reviews (7 customer reviews)

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Arbitrage Theory in Continuous Time (Oxford Finance) Arbitrage Theory in Continuous Time (Oxford Finance) 3.7 out of 5 stars (3)
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Book Description

January 14, 1999 0198775180 978-0198775188 0
Combining sound mathematical principles with the necessary economic focus, Arbitrage Theory in Continuous Time is specifically designed for graduate students, and includes solved examples for every new technique presented, numerous exercises, and recommended reading lists for each chapter.

Editorial Reviews


' This book is one of the best of a large number of new books on mathematical and probabilistic models in finance, postioned between the books by Hull and Duffie on a mathematical scale...This is a highly reasonable book and stikes a balance between mathematical development and intuitive explanation'Short Book Reviews

About the Author

Tomas Bjork, Professor, Department of Finance, Stockholm School of Economics.

Product Details

  • Hardcover: 328 pages
  • Publisher: Oxford University Press (January 14, 1999)
  • Language: English
  • ISBN-10: 0198775180
  • ISBN-13: 978-0198775188
  • Product Dimensions: 9.3 x 6.1 x 1 inches
  • Shipping Weight: 1.1 pounds
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (7 customer reviews)
  • Amazon Best Sellers Rank: #2,401,494 in Books (See Top 100 in Books)

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Customer Reviews

4.7 out of 5 stars
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Most Helpful Customer Reviews
27 of 27 people found the following review helpful
4.0 out of 5 stars Nicely Prepared Intermediate-Level Treatment May 5, 2005
Format:Hardcover|Verified Purchase
The author has put together an excellent text that will take readers of an elementary text like Hull's Options, Futures, and Other Derivatives to the next level. In the author's treatment, the power of stochastic calculus is brought to bear on the options pricing problem from the point of view of modern martingale theory, if not the complete mathematical rigor needed to establish all the results.

The text contains 26 chapters and 3 appendices. There is simply too much here to give a blow-by-blow account. So I'll try to hit the highlights.

The author gives intuitive definitions of some of the more heavy concepts from measure theory/Lebesgue integration, measure-theoretic probability theory and basic stochastic analysis. For the rigor, one need only look to the appendices, but the treatment is intuitive enough that can still follow along with only the occasionally glance to the back of the book.

Readers of Hull's text will find the first couple of chapters quite familiar, but starting in Chapter 4, stochastic integrals are (somewhat) formally introduced, along with the multi-dimensional version of Ito's change of variable rule. This is not overkill as the development of multi-factor term structure models later in the book benefits from this early development.
We note that these formulas are stated without proof, although they are motivated intuitively.

In the next chapter, stochastic differential equations are introduced and the Feynman-Kac representation is established as a nice application of Ito's rule. The chapter winds up with an intuitive treatment of Kolmogorov's forward & backward equations.
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8 of 9 people found the following review helpful
5.0 out of 5 stars intuitive introduction to option pricing November 9, 2004
By librayi
I agree with several reviewers above that the book is written in a style very helpful for students to understand the material.

It doesn't contain a lot of small details of financial markets like Hull's book, but the approach is very systematic. The derivations of formula for Barrier options is a nice example, Hull only lists a set of formula. The focus is on the theory, not on the practice. (No numerical method in the book). Bjork's book is very valuable for a student with very good math skills but want to learn the reasoning style for option pricing. It is a quick and enjoyable read.

A huge plus side of the book is to describe strategy before writing down all the proofs. This helps greatly. It can be contrasted with Duffie's book "Dynamic Asset Pricing Theory", which is written like a dry math book (well, I have to admit that Duffie's book is not an intro book)

Only thing I can think of that can be improved is typo in the book, too many wrong formula, especially in the second half of the book, luckily enough, they are obviously wrong so that one can still understand the topics. I also find that using SEK and mentioning street name of Britain are amusing for a student in U.S.
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13 of 16 people found the following review helpful
4.0 out of 5 stars Hell, I should have rated it 5 stars! May 25, 2002
If you're going to be introduced to Derivatives pricing and Quantitative finance in continuous time, you need some basics in probability theory, an elementary introduction to stochastic calculus and you need "bjork". It tells you the equation and how to understand it.
It's the best source for a complete understanding of the basics of arbitrage free pricing in continuous time; whether it's in complete or incomplete markets.
The best feature of this book is how the author invariably provides an "intuitive interpretation or explanation" to convey critical concepts. {Things like market price of risk in the context of interest rate modelling, change of measure etc...}
Why I rated the book 4 instead of 5?
I will not forgive "Tomas bjork" not to have covered the Libor Market Model; it's "THE" model and therefore should be covered in great details by any book of this calibre. A new edition of this book with the libor market model is needed.
Having said that, the coverage he gives to the popular short rate models is worth every read!
Msc Financial Engineering at ISMA Center, Reading - UK.
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9 of 12 people found the following review helpful
5.0 out of 5 stars An FE Bible November 7, 2001
The central text for IOE 552(financial Engineering I) at the University of Michigan. Halfway through the course and I really understand the application of Ito's Lemma and the Feynman-Kac stochastic representation theorem. This book has just the right mixture of narative story telling, and mathematical rigor. The derivations are accessible to those with a semester of advanced calculus and a semester of probability. Over and over, Bjork shows that the secret of success in Financial Engineering is "RAIL" which stands for the "Relentless Application of Ito's Lemma".
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