Product Description

The rewards and dangers of speculating in the modern financial markets have come to the fore in recent times with the collapse of banks and bankruptcies of public corporations as a direct result of ill-judged investment. At the same time, individuals are paid huge sums to use their mathematical skills to make well-judged investment decisions. Here now is the first rigorous and accessible account of the mathematics behind the pricing, construction and hedging of derivative securities. Key concepts such as martingales, change of measure, and the Heath-Jarrow-Morton model are described with mathematical precision in a style tailored for market practitioners. Starting from discrete-time hedging on binary trees, continuous-time stock models (including Black-Scholes) are developed. Practicalities are stressed, including examples from stock, currency and interest rate markets, all accompanied by graphical illustrations with realistic data. A full glossary of probabilistic and financial terms is provided. This unique, modern and up-to-date book will be an essential purchase for market practitioners, quantitative analysts, and derivatives traders, whether existing or trainees, in investment banks in the major financial centres throughout the world.

Product Details

• Amazon Sales Rank: #143035 in Books
• Published on: 1996-09-19
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 233 pages

Review
‘… a very readable and useful introduction to the pricing of derivatives … A recommendable book.’ Wil Schilders, ITW Nieuws

‘… the first rigorous and accessible account of the mathematics behind the pricing, construction and hedging of derivative securities.’ L’Enseignement Mathématique

Customer Reviews

Excellent introduction to mathematical finance.
I find this book definitely the best textbook available for a student with a quantitative background wishing to understand the basic ideas behind the theory of arbitrage pricing of derivative assets. Includes advanced topics such as HJM models for interest rates but remains understandable throughout the text. The book succeeds in maintaining a nice equilibrium between mathematical formalism and results of practical relevance.

One very important problem though is the TOTAL LACK of empirical examples and comments on the practical relevance of the various models introduced, which is crucial in any applied field. The text does not give any insight into the limits of the models presented and may lead the uninformed reader to jump to dangerous conclusions as to the applicability of some of the models presented.

There is also a certain amount of lack of scientific transparency involved: the reader is shown two similar-looking curves, one representing geometric Brownian motion and one representing the FTSE index as a 'justification' of the lognormal model for stock prices. The inadequacy of the lognormal model for stock prices is a well known fact with important consequences and should be mentioned in a text meant for students and beginners. For example, little is said about the volatility smile, market imperfections and related issues.

In short, this book is a good introduction to "mathematical finance" -considered as a branch of probability theory, probably the best introductory text written to this day. However it remains a book written by mathematicians with little relevance to finance or (real) financial markets.

Nevertheless, I enjoyed reading it!

One for pure mathies
"Options, Futures and Other Derivatives", Hull and/or "Financial Calculus: An Introduction to Derivative Pricing", Baxter & Rennie.

Either of these books individually would represent a good grounding in the mathematics underlying derivative pricing. The two books are very different to each other, though, and it is worth the reader considering his preferred approach before parting with cash. The main differences between the books are:

1. Baxter & Rennie follow a "pure maths" approach, basing the theory around a succession of mathematical theorems. Hull describes this approach in a later chapter, but builds up the theory using an "applied maths" approach, deriving a partial differential equation satisfied by derivative prices.

2. Hull includes background information on the derivative markets; Baxter & Rennie do not.

3. Hull describes how derivatives can be priced in practice, using techniques like Monte Carlo and trees; Baxter & Rennie do not.

If I had to choose one book, my personal preference would be for Hull, but this probably reflects my choice of degree courses. But having read Baxter & Rennie after Hull, my opinion is that the books compliment each other well. When things get so complicated that the intuitive realism of applied maths needs to give way to abstract pure maths (for example in considering quantos or yield curve models), the Baxter & Rennie approach is easier to follow.

A real introductory book
This books calls itself an introduction to derivative pricing. It does the job superbly. This is not a technical maths book nor is it full of financial jargon. It is a well written account of some of the basic ideas covered in an easy to understand manner.
You will understand why no arbitrage enforces a price and why other prices which intuitively seem right are in fact wrong. Moreover you will understand this in about 30 pages or less. It covers binomial trees, again in an easy way that first year maths undergraduate students should be able to understand. It moves on to continuous time, ito-formula and change of measures all the while keeping a strong focus on options. It has some exercises which are reasonable and instructive (even better it has solutions: a rare gift for these days). This is how introductory books should be written. Well done Rennie + Baxter!