THE MODIFIED TEMPERED STABLE DISTRIBUTION, GARCH MODELS
AND OPTION PRICING
Young Shin Kim
Svetlozar T. Rachev
Dong Myung Chung
Michele Leonardo Bianchi
Abstract: We introduce a new variant of the tempered stable distribution, named the modified
tempered stable (MTS) distribution and we develop a GARCH option pricing model with
MTS innovations. This model allows the description of some stylized empirical facts
observed in financial markets, such as volatility clustering, skewness, and heavy tails of stock
returns. To demonstrate the advantages of the MTS-GARCH model, we present the results of
the parameter estimation.
2000 AMS Mathematics Subject Classification: 60E07, 91B84.
Keywords and phrases: Option pricing, GARCH process, temper-
ed stable distribution, volatility clustering.