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Tempered Stable Processes with Time Varying Exponential Tails

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.
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https://hal-paris1.archives-ouvertes.fr/hal-03018495
Contributor : Raphael Douady <>
Submitted on : Sunday, November 22, 2020 - 6:39:18 PM
Last modification on : Tuesday, January 19, 2021 - 11:08:38 AM

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  • HAL Id : hal-03018495, version 1

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Young Shin Kim, Kum-Hwan Roh, Raphaël Douady. Tempered Stable Processes with Time Varying Exponential Tails. 2020. ⟨hal-03018495⟩

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