Tempered stable and tempered infinitely divisible GARCH models

被引:71
作者
Kim, Young Shin [1 ]
Rachev, Svetlozar T. [1 ,2 ,3 ]
Bianchi, Michele Leonardo
Fabozzi, Frank J. [4 ]
机构
[1] Univ Karlsruhe, Sch Econ & Business Engn, Karlsruhe, Germany
[2] Univ Calif Santa Barbara, Dept Stat & Appl Probabil, Santa Barbara, CA 93106 USA
[3] FinAnalytica INC, New York, NY USA
[4] Yale Univ, Sch Management, New Haven, CT USA
关键词
Tempered infinitely divisible distribution; Tempered stable distribution; Rapidly decreasing tempered stable distribution; GARCH model option-pricing; OPTIONS;
D O I
10.1016/j.jbankfin.2010.01.015
中图分类号
F8 [财政、金融];
学科分类号
0202 ;
摘要
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.
引用
收藏
页码:2096 / 2109
页数:14
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