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'… the first rigorous and accessible account of the mathematics behind the pricing, construction and hedging of derivative securities.' L'Enseignement Mathématique
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Financial market instruments can be divided into two distinct species. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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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!
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.
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!
An excellent book for the financial neophyte who knows about Brownian motion and the Ito Calculus. Read more
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