Tempered stable and tempered infinitely divisible GARCH models

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

Research output: Contribution to journalArticlepeer-review

65 Scopus citations


In this paper, we introduce a new GARCH model with an infinitely divisible distributed innovation. This model, which we refer to as the rapidly decreasing tempered stable (RDTS) GARCH model, takes into account empirical facts that have been observed for stock and index returns, such as volatility clustering, non-zero skewness, and excess kurtosis for the residual distribution. We review the classical tempered stable (CTS) GARCH model, which has similar statistical properties. By considering a proper density transformation between infinitely divisible random variables, we can find the risk-neutral price process, thereby allowing application to option-pricing. We propose algorithms to generate scenarios based on GARCH models with CTS and RDTS innovations. To investigate the performance of these GARCH models, we report parameter estimates for the Dow Jones Industrial Average index and stocks included in this index. To demonstrate the advantages of the proposed model, we calculate option prices based on the index.

Original languageEnglish
Pages (from-to)2096-2109
Number of pages14
JournalJournal of Banking and Finance
Issue number9
StatePublished - Sep 2010


  • GARCH model option-pricing
  • Rapidly decreasing tempered stable distribution
  • Tempered infinitely divisible distribution
  • Tempered stable distribution


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