Introduction to Stochastic Calculus Applied to Finance

Rating:
Summary: Too Much Exercises!!
Review: 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

Rating:
Summary: A good INTRODUCTION to ONE part of finance
Review: 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.

Rating:
Summary: A Mathematically Sophisticated But Frustrating Treatment
Review: 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.

Rating:
Summary: A stochastic approach of finance for engineers!
Review: 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.

Rating:
Summary: Clear and concise introduction to mathematical finance.
Review: 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.