Pricing and Hedging of Derivative Securities

Rating:
Summary: A book that can help you break the entry barrier..
Review: I read it with Rudin's"Principle of Mathematical Analysis" & Royden's "Real Analysis" by self-study.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.

Rating:
Summary: buy this book now!
Review: 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 imho!

Rating:
Summary: Learn continuous-time finance from this book!
Review: 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. Although somewhat limited in scope, 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. The level of mathematical sophistication is quite high, so don't expect anything like Neftci, Baxter and Rennie, Mikosch or Bjork. The level is the same of Duffie, but, while Duffie presents a lot of material and most of the time he doesn't provide proofs and explanations (which, personally, I find irritating), this book is limited to few selected topics, but they are explained at length.
Unfortunately, the perfect finance book has not yet been written (finance professionals seem to be too busy and well paid to write good books), but 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. Two good books to acompany this one might be Resnick's book on probability and Steele's book on stochastic calculus.

Rating:
Summary: Nielsen is simply amazing
Review: 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.
The three appendices (on measure and probability, the Lebesque integral, and the heat equation), and the first three chapters make the book as self-contained as is possible.
Synopsis: I do not know of a better book on this subject.

Rating:
Summary: Excellent textbook
Review: This book is excellent. As anyone interested in this field knows, there is a lot of high-level math. 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 like Neftci's book. Baxter & Rennie is better than Neftci, but not as good as Elliot & Kopp or Lamberton & Laperyre. All of the above I have studied to some extent, and Nielsen's book seemed to include all that these did AND to fill in the gaps. This is the first book I have seen to actually define 'numeraire'.

Make no mistake, to truly understand this material one has to make an investment in learning a good amount of math. The texts I recommend for real analysis are Royden (tops among all for ease and clarity) and Folland (more comprehensive, but very well written); for probability I recommend Resnick's new book which includes a good chapter on discrete-time martingales (much more readable than Chung) and the legendary text by Billingsley.

If you are willing to learn about 4 chapters of Royden and keep Resnick at your side, then this is the only book you need. If not, then start with Baxter and Rennie.

Rating:
Summary: Excellent textbook
Review: 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, such as "Arbitrage and Admissibility" and "The doubling strategy". As mentioned in the preface, the book is based on a doctoral-level course, 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. Finally, I have to mention the excellent editorial work done by Oxford University Press in producing this book, as compared to similar books published by Wiley.