Review of Pricing and Hedging of Derivative Securities. By Lars Tyge Nielsen. Textbook in continuous-time finance theory. Oxford University Press, 1999.
These are excerpts. Read the original reviews to get the complete story.
P. A. L. Embrechts, in Short Book Reviews, Publication of the International Statistical Institute:
This interesting text gives a very readable introduction to the mathematics of derivative pricing and hedging. The mathematical level is high, despite the fact that the author works in practice. The atter practical background clearly shows itself through the various pedagogical discourses, either through examples or discussions on ramifications of the methodology presented.
I found the author’s style of writing close to perfect: The material presented would make an excellent course. Mathematicians will get a lot out of the book because of the extra practical insight, but also because the author has taken great care to explain the sophisticated mathematics in a very cear and concise way. [...]
[...] All in all, I highly recommend this text to those prepared to invest the necessary time and effort for learning the subject of derivatives. It will no doubt become one of my favorites.
Bruce D. Grundy, in the Journal of Financial Research 23 (2000), 391-392:
This is a challenging and rewarding text. It will lead mathematics graduate students toward an interest in the problems of finance. It will lead finance graduate students toward the level of mathematical sophistication necessary to contribute to the literature in this field. It will also allow some academics currently teaching undergraduate and MBA derivatives courses to confirm or challenge their own often intuitive understanding of pricing, hedging, and arbitrage.
[...] Chapter 4 considers securities and trading strategies and the material here on admissible strategies and on changing the unit of account is a real strength of this text relative to others. [...]. [The] applications chapters make for comparatively light reading because copious examples throughout the earlier chapters focus on the Black-Scholes and one-factor interest rate setting. The quantity and quality of the numerous exercises and suggested solutions are another strength of this text.
[...] The preface states that one goal is to give the reader the background to read the journal literature with confidence. This promise is fulfilled as early as the notes to Chapter 1. [...] The text is worth buying for the notes to Chapter 1 alone. Once armed with this confidence, the reader will be much less intimidated by vague phrases in the literature such as “under the usual regularity conditions”.
In summary, this is a great doctoral text suitable for those in the most challenging of programs. [...]
Jerry Coakley, in the Economic Journal January 6, 2001:
[...] Although the book is generally mathematically demanding, it has the pedagogic merit that the author provides at the end of each chapter excellent intuitive explanations of all of the technical concepts employed and extended summaries of the material covered.
[...] To sum up, this book will prove valuable for those teaching graduate courses in continuous time finance and for researchers and practitioners who require access to a good reference book.
Marco Taboga, on Amazon.com:
Learn continuous time finance from this book: you won’t be disappointed. I have read almost all the most famous finance books and I must say that this is by far the best one of them. [...] it is masterfully written: everything is explained clearly and carefully. All statements are rigorously proved. I would say it is suitable both for beginners, having a minimum exposure to measure-theoretic probability and willing to spend some time on it, and for advanced students. Personally, I first read the book as a beginner and found it extremely useful, but even now, that I understand and know most of the material, I find it to be an invaluable reference. [...] this one is almost perfect. If you really want to understand quantitative finance, I strongly recommend that you invest a good amount of hours in studying this book. [...]
n-k-k, on Amazon.com:
Nielsen is simply amazing, September 28, 2001
Nielsen has written a virtually self-contained treatise on the subject. Reading this book was a beautiful learning experience: The author’s clarity of thought was striking; the examples made particular points transparent; and the exercises made invaluable contributions to understanding. [...] I do not know of a better book on this subject.
A reader from Australia, on Amazon.com:
This is an excellent textbook on financial mathematics. It is quite mathematical, but self contained, clearly and carefully written. The appendices are very well written condensed reviews of basic technical facts. The book also contains discussions of a topics that I’ve never seen anywhere else, [...]. [...] and the author clearly had the benefit of a large amount of feedback from students. Reading it, one can’t help notice the presence of a very large number of extra remarks and hints, inserted on every page in order to clarify what must have been a denser original text. [...]
Ken Oberg, on Amazon.com:
The mathematical finance book to own
This book is excellent. [...]. The author has included several appendices which cover the required background, and he only includes proofs that are helpful to overall understanding. All theorems without proofs have references to the standard math texts.
In comparison to other texts, it does not leave many important ideas to intuition [...]. This is the first book I have seen to actually define ‘numeraire’.
A reviewer on Amazon.com:
A book that can help you break the entry barrier
[...] In my view,you can replace Lamberton & Lapeyre with it. It is rigorous yet accessible for non-math major who is interested in derivatives pricing but frustrated with the high-level mathematics. Buy it and read it with your patience. It won’t make you disappointed.
Steven Hutt, on Amazon.com:
Buy this book now!
If you have a strong math background, you will not find a clearer, more rigorous exposition of arbitrage pricing. The writing style is light yet gives you a depth and insight other books miss. I’ve read all the usual texts, but this is the best by far [...]
A reviewer on Amazon.co.jp:
This book is a great book!!! which deals with financial mathematics in a mathematically rigorous manner. You have to read!! [...] real text book for financial math.
Imad E. S., on Amazon.fr:
Un ouvrage de base rigoureux et instructif
Le travail de Nielsen fait figure d’exception dans le monde de la finance où les livres infestés de coquilles voire d’erreurs ou en tout cas d’imprécisions sont la norme. [...] les aspects mathématiques sont abordés avec une grande rigueur (la qualité des annexes est de ce point de vue à saluer) sans tomber toutefois dans le travers du formalisme abscons et du jeu d’écriture qui n’explique rien, comme c’est parfois le cas dans le Musiela-Rutkowski. Avoir su allier précision, rigueur, recul et pédagogie (nombre de questions que l’on peut se poser sont anticipées dans des exemples détaillés) , telle est la prouesse de Nielsen qui fait de son ouvrage une référence à laquelle on n’a de cesse de se reporter lors de la lecture d’article plus avancés. On en vient alors à regretter qu’il n’ait pas traiter des sujets tels que la volatilité locale ou les modèles avec sauts tant on aurait aimer les redécouvrir sous sa plume.