TY - JOUR
T1 - Tempered stable and tempered infinitely divisible GARCH models
AU - Shin Kim, Young
AU - Rachev, Svetlozar T.
AU - Leonardo Bianchi, Michele
AU - Fabozzi, Frank J.
N1 - Funding Information:
We would like to acknowledge the helpful comments and suggestions of an anonymous referee and those of Gennady Samorodnitsky, who also helped us in formulating the problem of TID distributions. Rachev gratefully acknowledges research support through grants from the Division of Mathematical, Life and Physical Sciences, College of Letters and Science, University of California, Santa Barbara, the Deutschen Forschungsgemeinschaft, and the Deutscher Akademischer Austausch Dienst. Bianchi acknowledges that the views expressed in this paper are his alone and should not be attributed to those of his employer.
PY - 2010/9
Y1 - 2010/9
N2 - 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.
AB - 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.
KW - GARCH model option-pricing
KW - Rapidly decreasing tempered stable distribution
KW - Tempered infinitely divisible distribution
KW - Tempered stable distribution
UR - http://www.scopus.com/inward/record.url?scp=77954144448&partnerID=8YFLogxK
U2 - 10.1016/j.jbankfin.2010.01.015
DO - 10.1016/j.jbankfin.2010.01.015
M3 - Article
AN - SCOPUS:77954144448
SN - 0378-4266
VL - 34
SP - 2096
EP - 2109
JO - Journal of Banking and Finance
JF - Journal of Banking and Finance
IS - 9
ER -