Tempered stable distributions and processes in finance: Numerical analysis

Michele Leonardo Bianchi, Svetlozar T. Rachev, Young Shin Kim, Frank J. Fabozzi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

29 Scopus citations

Abstract

Most of the important models in finance rest on the assumption that randomness is explained through a normal random variable. However there is ample empirical evidence against the normality assumption, since stock returns are heavy-tailed, leptokurtic and skewed. Partly in response to those empirical inconsistencies relative to the properties of the normal distribution, a suitable alternative distribution is the family of tempered stable distributions. In general, the use of infinitely divisible distributions is obstructed the difficulty of calibrating and simulating them. In this paper, we address some numerical issues resulting from tempered stable modelling, with a view toward the density approximation and simulation.

Original languageEnglish
Title of host publicationMathematical and Statistical Methods for Actuarial Sciences and Finance
PublisherKluwer Academic Publishers
Pages33-42
Number of pages10
ISBN (Print)9788847014800
DOIs
StatePublished - 2010
EventInternational Conference on Mathematical and Statistical Methods for Actuarial Sciences and Finance, MAF 2008 - Venice, Italy
Duration: Mar 26 2008Mar 28 2008

Publication series

NameMathematical and Statistical Methods for Actuarial Sciences and Finance

Conference

ConferenceInternational Conference on Mathematical and Statistical Methods for Actuarial Sciences and Finance, MAF 2008
CountryItaly
CityVenice
Period03/26/0803/28/08

Keywords

  • Monte Carlo
  • Stable distribution
  • Tempered stable distributions

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    Bianchi, M. L., Rachev, S. T., Kim, Y. S., & Fabozzi, F. J. (2010). Tempered stable distributions and processes in finance: Numerical analysis. In Mathematical and Statistical Methods for Actuarial Sciences and Finance (pp. 33-42). (Mathematical and Statistical Methods for Actuarial Sciences and Finance). Kluwer Academic Publishers. https://doi.org/10.1007/978-88-470-1481-7_4