Journal
JOURNAL OF BANKING & FINANCE
Volume 34, Issue 9, Pages 2096-2109Publisher
ELSEVIER
DOI: 10.1016/j.jbankfin.2010.01.015
Keywords
Tempered infinitely divisible distribution; Tempered stable distribution; Rapidly decreasing tempered stable distribution; GARCH model option-pricing
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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. (C) 2010 Elsevier B.V. All rights reserved.
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