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Additive normal tempered stable processes for equity derivatives and power-law scaling

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  • Michele Azzone
  • Roberto Baviera

Abstract

We introduce a simple additive process for equity index derivatives. The model generalizes Lévy Normal Tempered Stable processes (e.g. NIG and VG) with time-dependent parameters. It accurately fits the equity index volatility surfaces in the whole time range of quoted instruments, including options with small time-horizon (days) and long time-horizon (years). We introduce the model via its characteristic function. This allows using classical Fourier pricing techniques. We discuss the calibration issues in detail and we show that, in terms of mean squared error, calibration is on average two orders of magnitude better than both Lévy and Sato processes alternatives. We show that even if the model loses the classical stationarity property of Lévy processes, it presents interesting scaling properties for the calibrated parameters.

Suggested Citation

  • Michele Azzone & Roberto Baviera, 2022. "Additive normal tempered stable processes for equity derivatives and power-law scaling," Quantitative Finance, Taylor & Francis Journals, vol. 22(3), pages 501-518, March.
    • Handle: RePEc:taf:quantf:v:22:y:2022:i:3:p:501-518
    DOI: 10.1080/14697688.2021.1983200
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    Cited by:

    1. Michele Azzone & Roberto Baviera, 2023. "Is (independent) subordination relevant in option pricing?," Papers 2307.08628, arXiv.org, revised Oct 2023.
    2. Michele Azzone & Roberto Baviera, 2023. "A fast Monte Carlo scheme for additive processes and option pricing," Computational Management Science, Springer, vol. 20(1), pages 1-34, December.
    3. Pascal François & Rémi Galarneau‐Vincent & Geneviève Gauthier & Frédéric Godin, 2022. "Venturing into uncharted territory: An extensible implied volatility surface model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(10), pages 1912-1940, October.

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