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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 model for equity index derivatives. The model generalizes well known L\`evy Normal Tempered Stable processes (e.g. NIG and VG) with time dependent parameters. It accurately fits Equity index implied volatility surfaces in the whole time range of quoted instruments, including small time horizon (few days) and long time horizon options (years). We prove that the model is an Additive process that is constructed using an Additive subordinator. This allows us to use classical L\`evy-type 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 L\`evy processes and Self-similar alternatives. We show that even if the model loses the classical stationarity property of L\`evy processes, it presents interesting scaling properties for the calibrated parameters.

Suggested Citation

  • Michele Azzone & Roberto Baviera, 2019. "Additive normal tempered stable processes for equity derivatives and power law scaling," Papers 1909.07139, arXiv.org, revised Jan 2022.
    • Handle: RePEc:arx:papers:1909.07139
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    File URL: http://arxiv.org/pdf/1909.07139
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    References listed on IDEAS

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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. repec:dau:papers:123456789/1380 is not listed on IDEAS
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    5. George, Thomas J & Kaul, Gautam & Nimalendran, M, 1991. "Estimation of the Bid-Ask Spread and Its Components: A New Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 623-656.
    6. Roll, Richard, 1984. "A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market," Journal of Finance, American Finance Association, vol. 39(4), pages 1127-1139, September.
    7. Jing Li & Lingfei Li & Rafael Mendoza-Arriaga, 2016. "Additive subordination and its applications in finance," Finance and Stochastics, Springer, vol. 20(3), pages 589-634, July.
    8. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2007. "Self‐Decomposability And Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 31-57, January.
    9. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
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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. 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.
    3. 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.

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