Item description for Introduction to Stochastic Calculus for Finance: A New Didactic Approach (Lecture Notes in Economics and Mathematical Systems) by Dieter Sondermann...
The large number of already available textbooks on stochastic calculus with specific applications to finance requires a justification for another contribution to this subject. The justifcation is mainly pedagogical. These lecture notes start with an elementary approach to stochastic calculus due to Fllmer, who showed that one can develop Ito's calculus "pathwise" as an exercise in real analysis. The text opens to students interested in finance a quick (but by no means "dirty") road to the tools required for advanced finance in continuous time, including option pricing by martingale methods, term structure models in a HJM-framework and the Libor market model. The reader is supposed only to be familiar with elementary real analysis (e.g. Taylor's Theorem) and basic probability theory. The text is also useful for mathematicians interested in the methods of modern mathematical finance without prior knowledge of advanced stochastic analysis.
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Reviews - What do customers think about Introduction to Stochastic Calculus for Finance: A New Didactic Approach (Lecture Notes in Economics and Mathematical Systems)?
simple but too superficial intro to stochastic calculus Nov 15, 2006
This book is intended to present a new pedagogical approach to stochastic calculus and its applications in finance. Prof. Sondermann makes an easy to follow introduction to quadratic variation, Ito's formula etc. using only basic tools from real analysis. After he introduces the Ito calculus and Girsanov theorem, he presents some applications in finance, like the risk neutral valuation, the currency options and the HJM model.
The book has the advantage that it introduces the stochastic calculus without relying on very heavy background. However, by doing this, it loses most of the precision of statements, and makes the book more suitable for bed-time reading. The book has no index term(!!), which is quite surprising for a mathematical book these days. Exercise problems are presented only for the introductory chapter on real analysis, none though for the material dealing with stochastic calculus. I do not see the reason why Prof. Sondermann decided on having exercises on the preliminaries and none on the main material, stochastic calculus. The book has also its share of typos, so be careful.
On the nice features, I liked the careful discussion of the currency options paradox (Siegel-Paradox), and the change of numeraire.
I think that Prof. Sondermann succeeded in presenting stochastic calculus in an easy way, and now readers might feel more comfortable to start reading a more advanced book on stochastic calculus.