Mathematical Techniques in Finance —— Tools for Incomplete Markets - Second Edition

Mathematical Techniques in Finance ranks as one of the best finance texts I've ever read. This book provides a good mix of theory and application which is well-suited for a master's level course and for practitioners. It fills the gap between undergraduate/MBA finance texts that focus on applications and Ph.D.-level texts that are in the theorem-proof style. To appreciate this book, I think the reader only needs to know calculus and a little linear algebra. The author is able to describe complex mathematical techniques in relatively easy, understandable terms. More importantly, the author highlights the important things to remember for each of the important concepts. For example, whether the absence of a Type I or Type II arbitrage is necessary for the existence of a solution when markets are complete or incomplete or which state variables play an important role in certain models. Moreoever, I have read many finance books, and this text's discussion of risk-neutral pricing and continuous time finance is one of the best. Aside from providing proofs for the more important concepts, Cerny also provides many numerical examples and MATLAB code (the MATLAB programs are available on the author's website) to implement many of the examples.

I had the great pleasure of attending Dr. Cerny's lectures in mathematical techniques in finance. The lectures were structured around this book and were accordingly brilliant. The book starts off gently, to great relief for those who need to cover more basic mathematics in discrete time, before moving on to continous time and later introducing concepts such as Matingales and Browninan Motion. The book shows you how to derive such as the Black Scholes Formula, and introduces the Ito formula which is extensively used in pricing options. Importantly, the book is clearly written and 'recycles' the exercises as it progresses from simple to more complex topics. I found this to be of great use since you already have an understanding of what the exercise is all about, intuitively and 'mechanically', and you can compare the methods and more readily understand what is going on in the more complex examples. This book does not require a heave maths background. As always, the more the better, however, you can easily make great use of this book only with an understanding of simple calculus like derivatives and integrals. A basic understanding of linear algebra will also prove beneficial. If you are looking for a book that will explain important concepts in finance, then this book is exactly what you are looking for.

This is a great little book. I would put it in my category of 'original' books on quant finance, which includes books written by Paul Wilmott, Mark Joshi, Rick Osband and Neftci. The reason being that the author uses a more informal style than most quant books and is very hands-on. If you're interested in understanding quant models and eventually applying them in the real world, then this is the kind of book you want. If you're looking for mathematical beauty and formalism, then look elsewhere. The editors could have done a better job with some of the flow and formatting - maybe next edition (it is sometimes hard to link the text to the figures and tables). Great book.

After reading million books on derivative pricing, this one is the only one which defenitely combines a practical approach to it. You'll start learning about all the maths you need and all the building blocks, all by examples. And suddenly on Chapter 11, it puts it all together and effortless you can price any option with any payoff you can imagine, I got impress withmyself. I work at Credit Suisse First Boston and we have it in all the Quant's desks.