Financial Calculus
Get to know your tool kit
The book seems to sell itself. Indeed, when I happened to leave it on top of my desk at Imperial College, there was soon a queue of research associates and postgraduate students begging to read it before it hit the bookshelves.Baxter and Rennie have done a formidable job in making difficult and/or counter-intuitive concepts accessible and user friendly.
To the prospective reader interested in the existing state of thinking about quantitative finance, I would say buy the book and read it from cover to cover, perhaps twice, if you do not know why nonmartingales are nontradables. If you know all about that and like to take Harrison-Pliska apart in your leisure time, buy the book regardless for ready reference.
Rudi Bogni
Times Higher Educational Supplement, Friday 24 January 1997
To read the whole review in full, click here (1200 words).
This witty, elegant, compact book breaks fresh ground. I think it represents the first of what may come to be a new generation of industry-oriented introductory books on derivative pricing theory, based on the use of modern probabilistic methods.In the past, books on derivative pricing have tended to be either distinctly academic or decidedly non-academic. The former include lengthy rigorous developments of the underlying theory in the theorem-proof style beloved of mathematicians. The latter tend to contain little more than a relatively soft introduction to the relevant finance theory, not going much further in mathematical content than, say, a simplified exposition of the rules of Itô calculus. For today's readers, this will no longer do, and a higher standard of direct exposition is required.
Baxter and Rennie have made an excellent step forward in satisfying these modern needs for a new generation of readers.
A colleague thought that Financial Calculus was perhaps a bit slapdash in places and suffered slightly from having little market minutiae in it - but nevertheless was now the best of its kind on the market. And so it is.
Lane Hughston
RISK Magazine, Vol 10, No 3, March 1997
To read the whole review in full, click here (850 words).
The stated intention of this book is to help to fill the gap between practice and theory in the rapidly expanding area of mathematical finance. Although it is a little light on the practical side on occasions (market practice is rarely mentioned and very few data are presented) it does, on the whole, achieve its aim.The earlier chapters contain several exercises and solutions are provided at the end of the book. In addition there is a comprehensive technical glossary, a summary of notation used a good list of further reading in the area of mathematical finance. This book is an essential part of the bridge between a simple understanding of market practice and the frankly intimidating approach adopted in the more mathematical texts in finance, and as such is to be highly recommended.
D.C. Bowie, Heriot-Watt University
Journal of the Royal Statistical Society A, Vol 160, Part 2, 1997
To read the whole review in full, click here (550 words).
Baxter and Rennie is uncompromisingly mathematical. It has no examples of data and hardly anything on the realism or otherwise of the models discussed. It also omits some major topics; there is only a brief mention, or nothing at all, of American options, exotic derivatives, numerical methods or market trading. This does not matter if the reader also has Hull to hand, but it would be a drawback of this book on its own. In fact, this concentration on the `core' models of mathematical finance works well, because the authors do succeed in presenting the martingale approach very clearly, as a less focused treatment might not have done.[There is a] difference between the PDE approach and the martingale approach to derivative pricing. The latter is where the real understanding comes from, while the former is an important computational tool, at least for stock models. Baxter and Rennie go straight for the martingale approach and apply it consistently and methodically to a variety of problems. They do derive the Black-Scholes PDE at one point, only to say: "Notoriously, this PDE, coupled with the boundary condition that V(s,T) must equal f(s), gives another way of solving the pricing equation."
In summary, Baxter and Rennie set out with the one clear purpose of explaining the martingale machinery, and do this very well indeed. Baxter and Rennie is an exceptionally clear introduction to the more advanced mathematics... The presentation of this "rocket science" machinery is excellent and very clear, and the new reader... might be well advised to buy Baxter and Rennie; for chapter 3 alone it would be worth it.
Angus Macdonald, Heriot-Watt University
Extracts from the British Actuarial Journal, to appear.
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