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Tempered stable processes with time-varying exponential tails

Author

Listed:
  • Raphaël Douady

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

  • Young Shin Kim
  • Kum-Hwan Roh

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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Suggested Citation

  • Raphaël Douady & Young Shin Kim & Kum-Hwan Roh, 2021. "Tempered stable processes with time-varying exponential tails," Post-Print hal-03512709, HAL.
    • Handle: RePEc:hal:journl:hal-03512709
    DOI: 10.1080/14697688.2021.1962958
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    Cited by:

    1. 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.
    2. Young Shin Kim & Frank J. Fabozzi, 2024. "Portfolio optimization with relative tail risk," Annals of Operations Research, Springer, vol. 341(2), pages 1023-1055, October.
    3. Young Shin Kim & Hyangju Kim & Jaehyung Choi, 2023. "Deep Calibration With Artificial Neural Network: A Performance Comparison on Option Pricing Models," Papers 2303.08760, arXiv.org.
    4. 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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