Tempered stable and tempered infinitely divisible GARCH models

Young Shin Kim, Svetlozar T. Rachev, Michele Leonardo Bianchi and Frank Fabozzi ()

No 28, Working Paper Series in Economics from Karlsruhe Institute of Technology (KIT), Department of Economics and Management

Abstract: In this paper, we introduce a new GARCH model with an infinitely divisible distributed innovation, referred to as the rapidly decreasing tempered stable (RDTS) GARCH model. This model allows the description of some stylized empirical facts observed for stock and index returns, such as volatility clustering, the non-zero skewness and excess kurtosis for the residual distribution. Furthermore, 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, these GARCH models allow to find the risk-neutral price process, and hence they can be applied to option pricing. We propose algorithms to generate scenario based on GARCH models with CTS and RDTS innovation. To investigate the performance of these GARCH models, we report a parameters estimation for Dow Jones Industrial Average (DJIA) index and stocks included in this index, and furthermore to demonstrate their advantages, we calculate option prices based on these models. It should be noted that only historical data on the underlying asset and on the riskfree rate are taken into account to evaluate option prices.

Keywords: tempered infinitely divisible distribution; tempered stable distribution; rapidly decreasing tempered stable distribution; GARCH model option pricing (search for similar items in EconPapers)
Date: 2011
New Economics Papers: this item is included in nep-ecm and nep-ets
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Citations: View citations in EconPapers (7)

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Journal Article: Tempered stable and tempered infinitely divisible GARCH models (2010)
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:kitwps:28

DOI: 10.5445/IR/1000023239

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