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|Title:||Tempered stable and tempered infinitely divisible GARCH models |
|Authors:||Kim, Young Shin|
Rachev, Svetlozar T.
Bianchi, Michele Leonardo
Fabozzi, Frank J.
|Issue Date:||2011 |
|Series/Report no.:||Working paper series in economics 28|
|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.|
|Subjects:||tempered infinitely divisible distribution|
tempered stable distribution
rapidly decreasing tempered stable distribution
GARCH model option pricing
|Persistent Identifier of the first edition:||urn:nbn:de:swb:90-232394|
|Document Type:||Working Paper|
|Appears in Collections:||Working Paper Series in Economics, Karlsruher Institut für Technologie (KIT)|
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