Tempered stable processes with time-varying exponential tails

In this paper, we introduce a new time series model having stochastic exponential tail. This is constructed based on the Normal Tempered Stable distribution with time-varying parameter. The captures tail, which generates volatility smile effect and term structure in option pricing. Moreover, describes of volatility. We empirically show skewness kurtosis by applying to analyze S&P 500 index return data. present Monte-Carlo simulation technique for parameter calibration prices. can see that tail makes better market prices calibration.