The Mathematics of Financial Derivatives: A Student Introduction

by Jeff Dewynne, P. Wilmott, Sam Howison

Finance is one of the fastest growing areas in the modern banking and corporate world. This, together with the sophistication of modern financial products, provides a rapidly growing impetus for new mathematical models and modern mathematical methods. Indeed, the area is an expanding source for novel and relevant real-world mathematics. In this book, the authors describe the modeling of financial derivative products from an applied mathematician's...

• Format: Paperback
• Language: English
• ISBN: 0521497892
• ISBN13: 9780521497893
• Release Date: September 1995
• Publisher: Cambridge University Press
• Length: 336 Pages
• Weight: 1.05 lbs.
• Dimensions: 0.7" x 6.0" x 9.0"

Customer Reviews

A good introduction to the PDE approach

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!

Very good introduction for physicists/applied mathematician

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?

Beautiful Text

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.

A very good for self-study!

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!visit vao-soongnern Nakhonratchasima, Thailand

Practical, easy-to-read and useful

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".