## Brownian Motion Calculus

### Ubbo F. Wiersema

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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. 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.

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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 Itō 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 Itō’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.

From the Inside Flap:

Wiersema has written a splendid book ... focusing on the core elements of the theory in a simplistic and operational manner. The reader is gently invited into the world of Ito integration and differentiation, where the material is carefully selected to highlight how the calculus functions rather than going into all theoretical details. The author provides many examples with relevance for financial applications, and each chapter ends with a good choice of exercises. The book is unique in its concise and inspiring style. This introduction to Brownian motion calculus is powerful, and highly recommended.

Professor Fred Espen Benth, Centre of Mathematics for Applications, Department of Mathematics, University of Oslo

Stochastic calculus fundamentals are covered with a high level of clarity in a consistent step-by-step manner. The book has the right blend of theory and practical applications allowing to develop a thorough understanding of the subject and to build a solid foundation for the future hands-on work.

Michael Zaidel, Senior Analyst – Quantitative Analytics, Toronto Dominion Bank Financial Group

The clear and open explanation of concepts combined with the many useful examples make this an invaluable reference both for students and professionals who need to gain an intuitive grasp and solid understanding of this vital subject. Wiersema's approachable style is sure to become a favourite amongst practitioners as it has amongst his students.”

Andrew Scourse, structured finance professional in a global bank

Ubbo's book is an extremely clearly written introduction to the important topic of applied stochastic calculus. In particular, it contains many illustrative worked-out examples and applications. This is a very well-balanced and structured guided-tour through the subject, where every step is carefully motivated and explained. Students will love this book!

Thorsten Rheinlander, Reader, London School of Economics

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## 1.Brownian Motion Calculus (Paperback)

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Book Description John Wiley and Sons Ltd, United Kingdom, 2008. Paperback. Condition: New. 1. Auflage. Language: English . Brand New Book. 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. 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. Seller Inventory # AAZ9780470021705

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Book Description John Wiley and Sons Ltd, United Kingdom, 2008. Paperback. Condition: New. 1. Auflage. Language: English . Brand New Book. 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. 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. Seller Inventory # AAZ9780470021705

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Book Description John Wiley and Sons Ltd, 2008. Condition: New. 2008. 1st Edition. Paperback. There are not many calculus books that are very accessible to students without a strong mathematical background and the large majority of financial derivatives students do not have a strong quantitative background. This book provides a short introduction to the subject with examples of its use in mathematical finance e. g pricing of derivatives. Num Pages: 330 pages, Illustrations. BIC Classification: PDE; PHF. Category: (P) Professional & Vocational. Dimension: 157 x 231 x 19. Weight in Grams: 488. . . . . . . Seller Inventory # V9780470021705

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Book Description John Wiley and Sons Ltd. Condition: New. 2008. 1st Edition. Paperback. There are not many calculus books that are very accessible to students without a strong mathematical background and the large majority of financial derivatives students do not have a strong quantitative background. This book provides a short introduction to the subject with examples of its use in mathematical finance e. g pricing of derivatives. Num Pages: 330 pages, Illustrations. BIC Classification: PDE; PHF. Category: (P) Professional & Vocational. Dimension: 157 x 231 x 19. Weight in Grams: 488. . . . . . Books ship from the US and Ireland. Seller Inventory # V9780470021705

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Book Description John Wiley & Sons, 2008. Condition: New. book. Seller Inventory # ria9780470021705_rkm