https://paris1.hal.science/hal-03018495Kim, Young ShinYoung ShinKimSBU - Stony Brook University [SUNY] - SUNY - State University of New YorkRoh, Kum-HwanKum-HwanRohHNU - Hannam UniversityDouady, RaphaëlRaphaëlDouadyCES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche ScientifiqueTempered Stable Processes with Time Varying Exponential TailsHAL CCSD2020Option PricingStochastic exponential tailVolatility of volatilityNormal tempered stable distributionLevy Process[QFIN.CP] Quantitative Finance [q-fin]/Computational Finance [q-fin.CP][STAT.AP] Statistics [stat]/Applications [stat.AP][QFIN.GN] Quantitative Finance [q-fin]/General Finance [q-fin.GN][QFIN.PM] Quantitative Finance [q-fin]/Portfolio Management [q-fin.PM][QFIN.PR] Quantitative Finance [q-fin]/Pricing of Securities [q-fin.PR][QFIN.RM] Quantitative Finance [q-fin]/Risk Management [q-fin.RM][QFIN.ST] Quantitative Finance [q-fin]/Statistical Finance [q-fin.ST]DOUADY, Raphael2020-11-22 18:39:182023-04-06 10:50:092020-11-23 13:17:11enPreprints, Working Papers, ...application/pdf1In this paper, we introduce a new time series model having a stochastic exponential tail. This model is constructed based on the Normal Tempered Stable distribution with a time-varying parameter. The model captures the stochastic exponential tail, which generates the volatility smile effect and volatility term structure in option pricing. Moreover, the model describes the time-varying volatility of volatility. We empirically show the stochastic skewness and stochastic kurtosis by applying the model to analyze S\&P 500 index return data. We present the Monte-Carlo simulation technique for the parameter calibration of the model for the S\&P 500 option prices. We can see that the stochastic exponential tail makes the model better to analyze the market option prices by the calibration.