THE MODIFIED TEMPERED STABLE DISTRIBUTION, GARCH MODELS AND OPTION PRICING∗ BY

Abstract. We introduce a new variant of the tempered stable distribu-tion, named the modified tempered stable (MTS) distribution and we de-velop 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