Financial modelling with jump processes. (English) Zbl 1052.91043

Cont, Rama; Tankov, Peter

Chapman & Hall/CRC Financial Mathematics Series. Boca Raton, FL: Chapman and Hall/CRC (ISBN 1-58488-413-4/hbk; 978-0-203-48521-7/ebook). xvi, 535 p. (2004).

The book is devoted to the theoretical, numerical and empirical research on the use of jump processes in financial modelling. After a short introduction to financial modelling beyond Brownian motion, in the first part (Chapters 2–5) the authors present a concise introduction to the mathematical theory of Lévy processes and related topics. The simulation and estimation of models with jumps are studied in Chapters 6 and 7. The third and longest part (Chapters 8–13) deals with the option pricing models based on stochastic calculus for jump processes. The models with jumps which are not in the exponential Lévy class are examined in the last part of the book. Throughout it, the authors offer significant contributions to the levels of mathematical details used to treat topics such as these.
This book provides a very well organized and clearly presented content, being based on pertinent references which include important results that belong to the authors.
The volume will be useful for the students, researchers in applied mathematics and quantitative finance as well as those interested in the study and the implications of discontinuous stochastic models and not only.

Reviewer: Vasile Postolică (Piatra Neamt)

MSC:

91-02	Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance
91G20	Derivative securities (option pricing, hedging, etc.)
91B70	Stochastic models in economics
91B24	Microeconomic theory (price theory and economic markets)
60G51	Processes with independent increments; Lévy processes
60J75	Jump processes (MSC2010)
62P05	Applications of statistics to actuarial sciences and financial mathematics
91G70	Statistical methods; risk measures

Keywords:

stochastic process; multidimensional and stochastic volatility models with jumps