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Tempered Stable Processes with Time Varying Exponential Tails

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  • Young Shin Aaron Kim

    (SBU - Stony Brook University [SUNY] - SUNY - State University of New York)

  • Kum-Hwan Roh

    (HNU - Hannam University)

  • Raphaël Douady

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

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 Aaron Kim & Kum-Hwan Roh & Raphaël Douady, 2020. "Tempered Stable Processes with Time Varying Exponential Tails," Working Papers hal-03018495, HAL.
    • Handle: RePEc:hal:wpaper:hal-03018495
    Note: View the original document on HAL open archive server: https://paris1.hal.science/hal-03018495
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    References listed on IDEAS

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    Cited by:

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    3. Tong Liu & Yanlin Shi, 2022. "Innovation of the Component GARCH Model: Simulation Evidence and Application on the Chinese Stock Market," Mathematics, MDPI, vol. 10(11), pages 1-18, June.

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    Keywords

    Option Pricing; Stochastic exponential tail; Volatility of volatility; Normal tempered stable distribution; Levy Process;
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