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Brownian Motion Calculus Paperback – 1 Aug 2008

4.5 out of 5 stars 4 customer reviews

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Product details

  • Paperback: 330 pages
  • Publisher: John Wiley & Sons; 1 edition (1 Aug. 2008)
  • Language: English
  • ISBN-10: 0470021705
  • ISBN-13: 978-0470021705
  • Product Dimensions: 15.2 x 2 x 22.7 cm
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Bestsellers Rank: 885,943 in Books (See Top 100 in Books)
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Product description

From the Back Cover

Brownian Motion Calculus

Ubbo Wiersema

Brownian Motion Calculus presents the basics of Stochastic Calculus with a focus on the valuation of financial derivatives. It is intended as an accessible introduction to the technical literature. The sequence of chapters starts with a description of Brownian motion, the random process which serves as the basic driver of the irregular behaviour of financial quantities. That exposition is based on the easily understood discrete random walk. Thereafter the gains from trading in a random environment are formulated in a discrete–time setting. The continuous–time equivalent requires a new concept, the It stochastic integral. Its construction is explained step by step, using the so–called norm of a random process (its magnitude), of which a motivated exposition is given in an Annex. The next topic is It s formula for evaluating stochastic integrals; it is the random process counter part of the well known Taylor formula for functions in ordinary calculus. Many examples are given. These ingredients are then used to formulate some well established models for the evolution of stock prices and interest rates, so–called stochastic differential equations, together with their solution methods. Once all that is in place, two methodologies for option valuation are presented. One uses the concept of a change of probability and the Girsanov transformation, which is at the core of financial mathematics. As this technique is often perceived as a magic trick, particular care has been taken to make the explanation elementary and to show numerous applications. The final chapter discusses how computations can be made more convenient by a suitable choice of the so–called numeraire. A clear distinction has been made between the mathematics that is convenient for a first introduction, and the more rigorous underpinnings which are best studied from the selected technical references. The inclusion of fully worked out exercises makes the book attractive for self study. Standard probability theory and ordinary calculus are the prerequisites. Summary slides for revision and teaching can be found on the book website www.wiley.com/go/brownianmotioncalculus.

About the Author

UBBO WIERSEMA was educated in Applied Mathematics at Delft, in Operations Research at Berkeley, and in Financial Economics and Financial Mathematics at the London School of Economics. He joined The Business School for Financial Markets (the ICMA Centre) at the University of Reading, UK, in 1997, to develop and teach its curriculum in Quantitative Finance. Prior to that, he was a derivatives mathematician at the merchant bank Robert Fleming in the City of London. Before that his career was focused in Operations Research in the US and Europe.

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Top Customer Reviews

Format: Paperback
Good summary of key concepts. Main fault is it has a tendency to make baffling leaps of logic, which I found very frustrating. For example, Ito's formula is quoted on page 76 but is rarely used in the examples (Taylor expansion being preferred for no apparent reason). When it is used (see page 137) it is hard to see how the results can be derived from the formula.

It's almost as if you need to know the derivations before reading the book, which defeats the purpose of buying the book.
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By PW on 4 May 2010
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This book provides much clarity and solidification of ideas for dealing with BM and stochastic calculus in general. It does not go into huge amounts of detail but provides a solid basis for getting started in this field. Well paced and clear, with many examples and many solved exercises. I don't use it for rigour but I use it often when I need an clear example of a specific concept. This is one of the only books in this field where the author truly assumes little knowledge beyond basic probability and is not trying to be another tediously rigorous academic. The author tends to cut through much of the scary looking background noise associated with more academic books and shows why stochastic calculus doesn't need to be hard or imposing (it is in fact neither - when taught well!). This is an entry level book but it's wonderful for explaining the important concepts so the reader can actually then take on a more academic book with less fear.
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Format: Paperback Verified Purchase
This book provides a very accessible introduction to stochastic calculus. Emphasis is on understanding the concepts and developing intuition rather than mathematical rigor. Like other reviewer said, it is one of the rare books on this topic which actually assume minimal prior knowledge of the subject - basic probability theory is enough. If you have felt intimidated by the math in some of the advanced stochastic calculus books, I strongly suggest that you start your journey here. It also has plenty of solved exercises, which make it ideal for self study. You can also email author for related excel files - thats what I did.

This book deserves much wider audience, highly recommended for people starting with stochastic calculus as well as for practitioners.
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excellent
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Most Helpful Customer Reviews on Amazon.com (beta) (May include reviews from Early Reviewer Rewards Program)

Amazon.com: 4.5 out of 5 stars 15 reviews
6 of 6 people found the following review helpful
5.0 out of 5 stars A must have for stochastic calculus course 28 Nov. 2010
By Yanpeng Guo - Published on Amazon.com
Format: Paperback Verified Purchase
I wish I had this book back in my school days. It is a must-have for college seniors or fresh graduate students who are interested in quantitative finance, as well as professionals on the street, like myself, who wants to review certain topics and concepts.

The book is an easy read, and it also has practice problems and solutions. This is the best part, typically stochastic calculus textbooks don't provide enough problems for us to solve, thus it is difficult to transform knowledge to skills. With practice problems, we always understand the topic better.

Read and do the practice problems in this book first, and it will prepare you well for the challenges ahead in quantitative finance.
2 of 2 people found the following review helpful
5.0 out of 5 stars Brownian Motion Calculus 17 Dec. 2011
By HWOO - Published on Amazon.com
Format: Paperback Verified Purchase
Presentation of concepts are exceptionally clear. Explanations on nice but important points are never missed out.
The flow of the contents of the book are very well structured. The level is just right for first beginners to learn the
subject .The solutions of the exercises at the back of the book are invaluable and particularly helpful to self-study.
All in all ,this is a book which I have hoped to have for years ,having given me the momentum to study the subject ,hopefully to complete reading it seriously from start and finish ! A book highly recommended for undergraduates who
first study Brownian Motion calculus.
2 of 2 people found the following review helpful
5.0 out of 5 stars A great book... 25 Jun. 2014
By Gordon Liu - Published on Amazon.com
Format: Paperback Verified Purchase
Very clear and intuitive, it covered all the important points that you need to know of Brownian motion in daily work as a quant analyst.
8 of 9 people found the following review helpful
5.0 out of 5 stars THE Introduction 22 July 2010
By Mehmet Zengin - Published on Amazon.com
Format: Paperback Verified Purchase
I read also Salih Neftci's book for stochastic calculus but this book is better. Mathematically it's more rigorous and very clear. It's an excellent introduction to stochastic calculus.
0 of 1 people found the following review helpful
5.0 out of 5 stars Exceptionally well written 6 May 2012
By Michael D. Colacino - Published on Amazon.com
Format: Paperback Verified Purchase
This book is a very clear, comprehensive introduction to stochastic calculus. It is long on intuition and is particularly useful for practitioners who need to apply these concepts. Very strong in its structure, this book provides derivations, examples, exercises and a very helpful set of appendices. If only all financial engineering books were written this well!
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