Customer Reviews

The Mathematics of Financial Derivatives: A Student Introduction

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Contrary to what many readers believe, this book explains the pricing of derivatives much better than Hull. Hull gives an overview of the mechanics and properties of the derivative pricing industry, along with its pricing methodologies, and this book provides an in depth method to one of the pricing methods.

Financial derivatives can be priced by a wide range of methodologies, among some the elegant equivalent martingale measure approach (or risk-neutral pricing), replication, multinomial tree approximation, Monte Carlo simulation, partial differential equations etc etc.

This book gives an excellent introduction, and an insight to the PDE approach. Although being a big fan of the Girsanov-change-of-measure method myself, these analytical methods often fail in the valuation of highly complex derivatives like the exotics. Pricing americans prove to be hard and inefficient too, even with simulation and the risk-neutral approach.

This is where PDE methods come in. Since most derivatives (or term structures) have a PDE describing its evolution, solving the PDE seems to be a good (or sometimes the best) way, no matter how complex the derivative can get. PDEs on the other hand, have very robust and easy methods for solving. Therefore, this book brings the reader through basic PDE solving methods, analytical solutions, techniques for fast and efficient numerical approximations as well as rigorous technical explanations for some of the mathematics of partial differential equations (which arise in the financial industry).

The authors are famous for their research in the field of Industrial and Applied Mathematics, and this book continues to be a classic for undergraduates in mathematics in Oxford. If you want to have an overview of the pde approach to option valuation, without the hassle of learning up Radon-Nikodým and martingales, I highly recommend this book!

I purchased this book sometmes ago and read it with interest. It's quite good introductory book for me (non-finance major). I can understand the rule of game they play in this subject. Mathematics background and computer program inthe book are well treated. Actually, there are a lot of equilivalent things to some physical science for most of these partial differential equation.

As my major is Polymer Physics, I encourage anyone who want to learn something more in this new financial area. This book give a key to open a door to finance!

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Before buying this book I opened some others which frightened me a little. As a pure mathematician, I wanted something that's mathematically 'juicy', and I really liked it. It's rigourous enough so that you know where the formulas come from, but fortunately not too formal (anyway there are great technical points for those who do want more details). This book has given me the motivation to learn more about financial derivatives, and I think that after I've read it, I'll probably go towards less mathematics-oriented books.

If you want an introduction, read another book like Hull. If you want to learn how to apply Partial Differential Equations (PDEs) approach to finance then it is a useful book. However, it is better to read an elementary PDEs book before reading this book. At least, learn how to solve parabolic PDEs analytically because the technical notes in the book would not help much.

The statement on the back this book that all the reader needs is some basic calc and a bit of probability is, as when you see it on most other similar books, false. To truly understand what is going on you need a prior knowledge of PDEs as well as some stochastic calculus. If you read this book after you have studies these you will learn a lot from it, but without this prior knowledge the book is too difficult to follow. I would recommend it to a reader who has seen the martingale approach to the subject before, and has at least studied ODEs and has a book on PDEs to refer to when the PDEs become too difficult to follow. The book manages to cover a lot, but you can't read a chapter and expect to have a good understanding from only reading the material. Most derivations, and even formulas, are left as exercises, and you need to complete at least 30% of the end of chapter exercises to firmly understand the material that the authors have covered. If you already have a good grasp of mathematical finance, this book can be a good way to further enhance your understanding, but don't buy this as an introductory book unless you are very strong in PDEs.

This is the classic introduction to financial derivatives, written from the point of view of pde's. Very suitable for mathematical physicists and applied mathematicians. Very lucidly written. I found it quite easy to gather information from it, though probably one will never really appreciate all the subtleties of the pde approach on first reading.

On a slightly different matter, one often reads hints to the effect that the martingale approach is more powerful than the pde approach. It would be great if anyone could tell us, using concrete examples why exactly that is the case. Do we really need all of the measure theory celebrated in martingale-based textbooks in order to valuate anything? If yes, then how come that none of that shows up in the pde approach?

Wilmott's book was one of the first to tackle options pricing from a PDE point of view. The original book (now out of print) was a little more detailed and later superseded by this cheaper "Student Edition" overview on one hand and the "Wilmott on Quantative Finance" 3-volume set on the other hand. A per its title, this is an applied mathematics book, and therefore a minimal level of math is expected from the reader (so please, do not compare with Hull...).

Taking a PDE approach, the book aims at presenting various methods for pricing financial options. While the first few chapters are pretty good at skimming the surface of the theory and laying down the key principles of options pricing, the book, in general, lacks depth. Many results (prices of barrier, lookback, asian, etc...) are given without real development or simply with a little "hand-waving". As soon as things get a little complicated, Wilmott just outlines the way forward and drops buzz-words.

In that sense, the book, while attempting go beyond introductory level topics in some details, does not provide great insight into the more difficult areas of option pricing and, lacking courage, simply goes through what has become the standard presentation without adding much value. Not for beginers, but not for more advanced readers either !

It is nonetheless an acceptable quick overview if you are looking for a refresher of key concepts. For a more thorough mathematical introduction to options pricing, You-Lan Zhu's book (for example) does a much better job at covering the PDE approach rigorously (proving for example some of the convergence criterias for the finite difference method, covering the linear complementarity approach as well as presenting other numerical techniques) without being overly formal.

This book is an excellent introduction to the use of finite difference and binomial methods to the pricing of equity options - regular and exotic/path-dependent. Requires only undergraduate calculus, and provides some intuition about the finance. Has exercises and solutions for people who want to learn. The "parent" book (Option pricing: mathematical models and pricing by P. Wilmott) has more information (although a little pricey!), is in fact used by financial "quants".

My professor recommended this book to me as one of the important readings. At first sight, it looked quite challenging, even though I have both economic and engineering background.

It took me a while to realize that it requires hands-on and self calculations (even repetition) to really grasp the concepts. Although the reading is difficult, that process is rewarding in two main ways. First, after first few chapters readers will forget the fear of math. Second, when the math and finance treatments converge the understanding will become solid. In so doing, the book has succeeded in "introducing" this world to audience. My suggestion is when reading this, one would need pen, paper, formula table and a running computer. Reading for fun is not the style of this.

Since the first reading of this, I bought many others, but still found this extremely clear and well written. Don't be afraid of their math notations as the core remains (replacing one symbol with another should not terrify us). His approach of PDE is clearly well-known and to me most comprehensible. In this sense, the book is mathematically more familiar to people coming out of normal university math.

Strongly recommend this book to students and professionals. Besides finance concepts, it also helps refresh math skills of readers. You will share my opinion after reading. Another plus is it is quite inexpensive.

I actually returned this book, but I have it now from somewhere else and the book is very helpful with math finance. There are good examples of how to work out each proof. It is just very helpful