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Tempered Stable Processes with Time Varying Exponential Tails

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  • Young Shin Kim
  • Kum-Hwan Roh
  • Raphael Douady
Abstract
In 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.

Suggested Citation

  • Young Shin Kim & Kum-Hwan Roh & Raphael Douady, 2020. "Tempered Stable Processes with Time Varying Exponential Tails," Papers 2006.07669, arXiv.org, revised Aug 2020.
  • Handle: RePEc:arx:papers:2006.07669
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    References listed on IDEAS

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    4. Young Shin Kim, 2022. "Portfolio optimization and marginal contribution to risk on multivariate normal tempered stable model," Annals of Operations Research, Springer, vol. 312(2), pages 853-881, May.

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