The Mathematics of Financial Derivatives: A Student Introduction (Paperback)

~ (Author), Sam Howison (Author), Jeff Dewynne (Author) "This book is about mathematical models for financial markets, the assets that are traded in them and, especially, financial derivative products such as options and..." (more)
Key Phrases: linear complementarity form, average strike option, possible asset prices, Technical Point, Further Reading, Asset Price Random Walks (more...)

Editorial Reviews

Review

'The layout is good and clear, so is the style of notation ... overall this is an excellent tool for both mathematicians interested in the world of finance as well as finance practitioners keen to rebuild the foundations of their knowledge.' Rudi Bogni, Times Higher Education Supplement

'The book is pleasantly readable and gives a good introduction.' C. Praagman, ITW Nieuws

Product Description

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 viewpoint, from modeling to analysis to elementary computation. The authors present a unified approach to modeling derivative products as partial differential equations, using numerical solutions where appropriate. The authors assume some mathematical background, but provide clear explanations for material beyond elementary calculus, probability, and algebra. This volume will become the standard introduction for advanced undergraduate students to this exciting new field.

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Product Details

• Paperback: 317 pages
• Publisher: Cambridge University Press (September 29, 1995)
• Language: English
• ISBN-10: 0521497892
• ISBN-13: 978-0521497893
• Product Dimensions: 8.9 x 6 x 0.6 inches
• Shipping Weight: 1.9 pounds (View shipping rates and policies)
• Average Customer Review: 3.4 out of 5 stars  See all reviews (22 customer reviews)
• Amazon.com Sales Rank: #361,210 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

12 of 13 people found the following review helpful:

5.0 out of 5 stars A very good for self-study!, July 21, 1999

By A Customer

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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11 of 12 people found the following review helpful:

5.0 out of 5 stars A good introduction to the PDE approach, October 9, 2005

By	Mathematician (Oxford, UK) - See all my reviews

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!

9 of 10 people found the following review helpful:

4.0 out of 5 stars Good introduction for mathematicians interested in Finance, May 26, 1999

By A Customer

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.