Tools for Computational Finance

1. Front Matter

   Pages I-XIV

   PDF

2. Modeling Tools for Financial Options

   • Rüdiger Seydel

   Pages 1-50

3. Generating Random Numbers with Specified Distributions

   • Rüdiger Seydel

   Pages 51-77

4. Numerical Integration of Stochastic Differential Equations

   • Rüdiger Seydel

   Pages 79-98

5. Finite Differences and Standard Options

   • Rüdiger Seydel

   Pages 99-140

6. Finite-Element Methods

   • Rüdiger Seydel

   Pages 141-164

7. Pricing of Exotic Options

   • Rüdiger Seydel

   Pages 165-189

8. Back Matter

   Pages 191-227

   PDF

Basic principles underlying the transactions of financial markets are tied to probability and statistics. Accordingly it is natural that books devoted to mathematical finance are dominated by stochastic methods. Only in recent years, spurred by the enormous economical success of financial derivatives, a need for sophisticated computational technology has developed. For ex­ ample, to price an American put, quantitative analysts have asked for the numerical solution of a free-boundary partial differential equation. Fast and accurate numerical algorithms have become essential tools to price financial derivatives and to manage portfolio risks. The required methods aggregate to the new field of Computational Finance. This discipline still has an aura of mysteriousness; the first specialists were sometimes called rocket scientists. So far, the emerging field of computational finance has hardly been discussed in the mathematical finance literature. This book attempts to fill the gap. Basic principles of computational finance are introduced in a monograph with textbook character. The book is divided into four parts, arranged in six chapters and seven appendices. The general organization is Part I (Chapter 1): Financial and Stochastic Background Part II (Chapters 2, 3): Tools for Simulation Part III (Chapters 4, 5, 6): Partial Differential Equations for Options Part IV (Appendices A1 ... A7): Further Requisits and Additional Material.

• Derivative pricing
• Finance
• Numerical integration
• Optionen
• Stochastic Differential Equations
• derivatives
• differential equation
• exotische Optionen
• financial markets
• finite element method
• mathematical finance
• numerics
• probability
• rating
• statistics
• quantitative finance

 

"In an increasingly crowded field of financial engineering titles, Seydel's Tools for Computational Finance stands out as filling an unmet need. It is an intermediate level text with an extremely practical focus. ... This is the kind of book you can read quickly, gaining a broad understanding of practical techniques of financial engineering. On the other hand, you can go through it slowly, working through all the examples and exercises in order to gain indepth practical knowledge you can use on the job. "

www.riskbook.com

 

"Remarkably, Seydel addresses students of both mathematics and business, presumes only minimal background in either subject, yet ventures deep into the subject in little more than 200 pages. Compare the longer books Mathematics of Financial Markets, by R.J. Elliott and P.E. Kopp (1999), or Methods of Mathematical Finance, by I. Karatzas and S.E. Shreve (1998), which presume research-level preparation in probability theory, delve deeper into theoretical issues, but ignore numerics. On the mathematical side, Seydel covers stochastic processes, random number generation, stochastic differential equations, finite differences, and finite elements. On the financial side, he treats put and call options of so-called American, European, and Asian types. A Web site provides additional material, including colored figures. Summing Up: Highly recommended. "

CHOICE

 

"Seydel has sought a compromise between justifying his results and avoiding formal proofs. I think he has struck a healthy balance, and I enjoyed reading the book.

...

Hull´s book teaches how to write the equations and Seydel´s teaches how to solve them"

Physics Today

 

"In my opinion, this book is mainly tailored to financial researchers and practitioners with an applied mathematics or engineering background. Various methods are introduced froma problem-solving point of view, been eventually formulated and summarised as algorithms which are offered for straightforward implementation in computer programmes. This expository style, which is similar to Kloeden´s and Platen´s 'Numerical Solutions of SDEs through computer experiments', makes the book unique among others and will definitely attract a broad range of readers coming from the financial academia or practice.

Quant Notes

 

"This book is very easy to read and one can gain a quick snapshot of computational issues arising in financial mathematics. Researchers or students of the mathematical sciences with an interest in finance will find this book a very helpful and gentle guide to the world of financial engineering."

SIAM review (46, 2004)

From the reviews of the third edition:

"Tools for Computational Finance is a book on numerical methods for pricing financial derivative products. … the author concentrates on how to provide numerical solutions to the problem of pricing. Exercises are provided at the end of each chapter and they follow and complement the text very well. In my opinion the book is more for practitioners … . it does guide us in a right direction and I think it could be valuable even for an academic." (Ita Cirovic Doney, MathDL-online, October, 2006)

• Institute of Mathematics, University of Köln, Köln, Germany

  Rüdiger Seydel

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