Monte Carlo Methods in Finance

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Monte Carlo Methods in Finance

By: Peter Jaeckel

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Product code: 14474
ISBN: 047149741X
304 pages
Format: Hb
Published by: John Wiley & Sons, 2002, 1st edition
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Description of Monte Carlo Methods in Finance
Monte Carlo Methods in Finance adopts a practical flavour throughout, the emphasis being on financial modelling and derivatives pricing. Numerous real world examples help the reader foster an intuitive grasp of the mathematical and numerical techniques needed to solve particular financial problems. At the same time, the book tries to give a detailed explanation of the theoretical foundations of the various methods and algorithms presented.

Monte Carlo methods have been used in the financial community for many years for addressing complex financial calculations. Recent advances by both practitioners and academic researchers in the area of fast convergence methods, together with the improvements achieved by the manufacturers of computer hardware, make Monte Carlo simulations more and more frequently the method of choice. In this long needed book on modern Monte Carlo methods in finance, Peter Jaeckel provides an introduction to many of the leading edge techniques available.

Monte Carlo Methods in Finance is an important reference for those working in investment banks, insurance and strategic management consultancy. Of particular importance are the many known variance reduction methods, and they are duly covered, not only in their own right, but also with respect to their potential combinations, and in the direct context of realistic applications. Most notably, the issue of the reliability of low-discrepancy numbers in high dimensions is discussed in detail. The book also contains an introduction to the theory of copul¾ as an extension to the modelling of correlation of financial securities. An entire chapter is dedicated to the evaluation of interest rate derivatives in the Brace-Gatarek-Musiela/Jamshidian framework by the aid of fast-convergence Monte Carlo simulations. What's more, for the first time, this book also gives a description of the construction of non-recombining trees.

Whilst non-recombining trees are usually not viable in a production environment, they often are the very tool of last resort when Monte Carlo approximations to problems such as Bermudan swaptions are to be tested, and the tricks for the construction of non-recombining trees presented in this book are invaluable for that purpose.


The book is packed with numerous examples using real world data and is supplied with a CD to aid in the use of the examples.

Monte Carlo Methods in Finance - Chapter headings
Contents
Preface
Mathematical Notation

1. Introduction

2. The mathematics behind Monte Carlo methods

3. Stochastic dynamics

4. Process driven sampling

5. Correlation and co-movement

6. Salvaging a linear correlation matrix

7. Pseudo-random numbers

8. Low-discrepancy numbers

9. Non-uniform variates

10. Variance reduction techniques

11. Greeks

12. Monte Carlo in the BGM/J framework

13. Non-recombining trees

14. Miscellanea

Bibliography
Index