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Tempered stable distributions and processes in finance: numerical analysis

In: Mathematical and Statistical Methods for Actuarial Sciences and Finance

Author

Listed:
  • Michele Leonardo Bianchi

    (Bank of Italy, Specialized Intermediaries Supervision Department)

  • Svetlozar T. Rachev

    (University of Karlsruhe and KIT, School of Economics and Business Engineering
    University of California, Department of Statistics and Applied Probability
    FinAnalytica, INC)

  • Young Shin Kim

    (University of Karlsruhe and KIT, School of Economics and Business Engineering)

  • Frank J. Fabozzi

    (Yale School of Management)

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 againstthe normality assumption, since stockreturns 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.

Suggested Citation

  • Michele Leonardo Bianchi & Svetlozar T. Rachev & Young Shin Kim & Frank J. Fabozzi, 2010. "Tempered stable distributions and processes in finance: numerical analysis," Springer Books, in: Marco Corazza & Claudio Pizzi (ed.), Mathematical and Statistical Methods for Actuarial Sciences and Finance, pages 33-42, Springer.
    • Handle: RePEc:spr:sprchp:978-88-470-1481-7_4
    DOI: 10.1007/978-88-470-1481-7_4
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