Tempered stable and tempered infinitely divisible GARCH models |
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Authors: | Young Shin Kim Svetlozar T. Rachev Michele Leonardo Bianchi Frank J. Fabozzi |
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Affiliation: | 1. School of Economics and Business Engineering, University of Karlsruhe and KIT, Germany;2. Department of Statistics and Applied Probability, University of California, Santa Barbara, United States;3. FinAnalytica INC., New York, NY, United States;4. Specialized Intermediaries Supervision Department, Bank of Italy, Italy;5. Yale School of Management, New Haven, CT, United States |
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Abstract: | 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. |
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Keywords: | C4 G12 G13 |
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