Volume IX


Tichý, T. (2011).
Lévy Processes in Finance: Selected applications with theoretical background.
Series on Advanced Economic Issues, Vol. 9.
Ostrava: VŠB-TU Ostrava, 146 s, vazba měkká.
ISBN 978-80-248-2536-6.
ukázka (240 kB, pdf)

The publication is focused on a modern tool of financial modeling – Lévy processes and their applications in finance. Lévy process is any continuous-time process that starts at zero, can consists of jumps (although, it is cadlag) and corresponds to infinitely divisible probability distribution. It follows that such group of processes is very broad. In finance, however, a special attention is paid to Lévy processes defined in terms of subordinated Brownian motions. Such kind of processes allows one to fit also the higher moments of the empirical distribution of financial assets (log)-returns, skewness and kurtosis in particular.

The book is divided into four parts. The first part of the book provides the reader the basic theoretical background (mathematical), while some (financial) specialities were moved to appendices. Next three parts are focused on different applications of Lévy models in finance. In particular, Part II is focused on model presentation, Part III on market risk estimation, and Part IV on option pricing and corporate hedging.   

The publication was written with the support provided by IT4Innovations Centre of Excellence and the SGS project of VSB-TU Ostrava SP2011/7. The support is greatly acknowledged. 

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