Customer Reviews

Introduction to Stochastic Calculus Applied to Finance (Chapman & Hall/CRC Financial Mathematics Series)

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As precisely mentioned in the title, this book is only an introduction; and it is not an introduction to finance, but to stochastic calculus applied to finance.

The buyer of this book should therefore be aware of three facts:

1. After having read this book you are not (yet) an expert on stochastic calculus applied to finance. You have to continue with other books mentioned in Lamberton/Lapeyre. But this book is an excellent framework that leads you to many important results, omiting proofs that are only technical.

2. Mathematics is used in many other areas of Finance too (Time Series Analysis for example). What is treated in this book is only a very small part of Finance Mathematics, but an important one.

3. One should read another book with more economic background at the same time.

The authors begin with discrete-time models to present many important ideas in a (mathematically) simple environment before treating the contiuous models. Introduction to stochastic integration and stochastic differential equations is brief. Stochastic integration is only with respect to the standard browning motion. After having reached the Black-Scholes model and american options, the approach via partial differential equations is treated, followed by interest rate models, models with jumps and, a good idea: a chapter on simulations.

The book has very few mistakes, no important ones, only a strange layout failure on pages 6 to 7.

So I highly recommend this book as an INTRODUCTION to ONE important part of finance mathematics if read in combination with another book with more economic background. It can especially be used for upper graduate student seminars or as a basis for lecture courses.

The book is a translation of a French Text. Generally, the exposition is mathematically sophisticated and flows well. However, many of the interesting and important results are given as exercises and long problems with many parts which can be frustrating (& irritating). In fact, I would estimate that a third of the book consists of these exercises and problems. The book should be used as a companion to other more basic books on option pricing like "Financial Calculus" by Baxter et al.

Introduction to Stochastic Calculus Applied to Finance, translated from French, is a widely used classic graduate textbook on mathematical finance and is a standard required text in France for DEA and PhD programs in the field.

Most folks familiar with Steve Shreve's Stochastic Calculus Models for Finance will be surprised at its brevity, for this work is aimed at different audiences.

Whereas Shreve's work is aimed at mathematicians and physicists who are coming to finance, and building on the commonalities of understandings of time series and data sets and signals, Lamberton & Lapeyre's work is aimed at an audience of mathematically trained engineers, who look at data sets as information for solving problems. Shreve's work, is, therefore, to help people come up with mathematical proofs, and L&L's is to help people solve problems.

Both probabilistic and partial differential equation approaches are covered, so both those from electrical and telecommunication engineering and mechanical engineering will be satisfied and on familiar ground. Numerical and algorithmic methods are also covered for those with systems analysis and operations management backgrounds.

This book, however, is decidedly for those who have had significant mathematical training. Whereas with Hull, Wilmott, Neftci, or Joshi you can play around with their approaches almost instantly in Excel or other programming tools (VBA, C, etc.), Lamberton and Lapeyre's work is for those who think out loud with a white board and others do the dirty work of coding. This work lacks specific examples, data sets, etc. Which makes it difficult to place. Its clarity and brevity are welcome, and it expands the knowledge beyond Hull of those who are not trained in math and came up the practical coding grunt side of quantfin. But it also is not a complete theoretical treatment for the first string math and theory set.

In short, the book is what it is: a short primer on a large area of mathematics in finance for those well-trained in a variety of engineering and applied mathematical subjects. In other words, this book is for the French, because all the best French students are always Engineers first and something else afterwards. If you also happen to be trained as an engineer and find Hull, Wilmott, Joshi & Neftci too easy, and Shreve too hard, then this is the book for you. Or if you are like me, and you've banged your head against this stuff for years just through the happenstance of your career and want to see how a mathematician writes about your gritty world, this is a great book for shedding light in areas filled with cobwebs.

The french initial version of this book has been one of my first technical papers that deal with stochastic calculus towards finance. It is written by and for engineers I must admit, but students in actuarial sciences (like me) won't be lost by so many formulas and equations if they agree to read with a piece of paper and a pencil on the hand. I have worked on the Vasicek's model and the simulations described have helped me a lot. Too bad that the lattice model is not explored. Anyway it is a good preparation before the opening of "Brownian Motion and Stochastic Calculus" from Karatzas & Shreve.

A compact & rigorous book on the mathematics of financial derivatives.However, it's not a best buy for having too much exercises . I would recommend Neftci's or Baxter's book for newcomers

I am quite familiar with this book since I enjoyed it when it was used (along with many other good books as it should) in Purdue Computational Finance program. I got to do a number of exercises from it. Some Matlab code is available on my website (click on my name above).

This book, translated from French, is by now a classic graduate textbook on mathematical finance, and provides a clear and concise introduction to the basic and important aspects of the theory. Although one of the first textbooks on the subject, it still remains in my opinion one of the best.

The book has been written for engineering students not mathematicians and avoids the theorem/proof format, going straight to essentials.

Also, while most textbooks on mathematical finance exclusively adopt either a probabilistic (like Baxter & Rennie) or a PDE approach to the theory (Wilmott et al, Wilmott), this book maintains the balance between the two aspects. Moreover, it does not neglect numerical methods and gives details on several algorithms for option pricing ( trees, Finite Difference, Monte Carlo) Finally, and perhaps this point is very important, the book maintains a reasonable volume while treating all these topics AND maintaining a high level of scientific rigor: all statements and notations are precise and oversimplification is avoided. Advanced topics such as variational inequalities for American options and HJM theory of interest rates are also included.

Some drawbacks of the book are: - a complete absence of empirical data/ real life figures - no description of various kinds of derivative products, why they are used,... But then, what can you ask for in such a small volume?

If you are an engineering/maths student and you want to discover what mathematical finance is about, I recommend you this book instead of John Hull's book.