Tempered stable distributions and processes in finance: Numerical analysis

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

doi:10.1007/978-88-470-1481-7_4

Tempered stable distributions and processes in finance: Numerical analysis

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

Mathematics and Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English
Title of host publication	Mathematical and Statistical Methods for Actuarial Sciences and Finance
Publisher	Kluwer Academic Publishers
Pages	33-42
Number of pages	10
ISBN (Print)	9788847014800
DOIs	https://doi.org/10.1007/978-88-470-1481-7_4
State	Published - 2010
Event	International Conference on Mathematical and Statistical Methods for Actuarial Sciences and Finance, MAF 2008 - Venice, Italy Duration: Mar 26 2008 → Mar 28 2008

Publication series

Name	Mathematical and Statistical Methods for Actuarial Sciences and Finance

Conference

Conference	International Conference on Mathematical and Statistical Methods for Actuarial Sciences and Finance, MAF 2008
Country	Italy
City	Venice
Period	03/26/08 → 03/28/08

Keywords

Monte Carlo
Stable distribution
Tempered stable distributions

Access to Document

10.1007/978-88-470-1481-7_4

Link to publication in Scopus

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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

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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.",

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Bianchi, ML, Rachev, ST, Kim, YS & Fabozzi, FJ 2010, Tempered stable distributions and processes in finance: Numerical analysis. in Mathematical and Statistical Methods for Actuarial Sciences and Finance. Mathematical and Statistical Methods for Actuarial Sciences and Finance, Kluwer Academic Publishers, pp. 33-42, International Conference on Mathematical and Statistical Methods for Actuarial Sciences and Finance, MAF 2008, Venice, Italy, 03/26/08. https://doi.org/10.1007/978-88-470-1481-7_4

Tempered stable distributions and processes in finance : Numerical analysis. / Bianchi, Michele Leonardo; Rachev, Svetlozar T.; Kim, Young Shin; Fabozzi, Frank J.

Mathematical and Statistical Methods for Actuarial Sciences and Finance. Kluwer Academic Publishers, 2010. p. 33-42 (Mathematical and Statistical Methods for Actuarial Sciences and Finance).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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