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Additive Processes with Bilateral Gamma Marginals

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  • Dilip B. Madan
  • King Wang

Abstract

The Sato process associated with self decomposable laws at unit time is further generalized to an additive process with arbitrary innovation term structures. A second generalization to additive processes consistent with bilateral gamma marginal distributions is also made. The Sato process is a parametric special case of the two generalizations. This feature is exploited in defining calibration starting values. Calibration results are presented for $$1255$$1255 days of daily data on SPY options. The deterministic innovation variance model makes a median improvement of $$15\% $$15% in root-mean-square error over the Sato process. The comparable value for the general additive process is $$40\%.$$40%. The Sato process relative to the general additive process overprices negative moves and underprices positive ones. The underpricing of negative moves decreases with maturity. On the positive side, the overpricing decreases with maturity. For negative moves, the overpricing is larger for smaller moves, while for positive moves the underpricing is larger for the larger moves.

Suggested Citation

  • Dilip B. Madan & King Wang, 2020. "Additive Processes with Bilateral Gamma Marginals," Applied Mathematical Finance, Taylor & Francis Journals, vol. 27(3), pages 171-188, May.
    • Handle: RePEc:taf:apmtfi:v:27:y:2020:i:3:p:171-188
    DOI: 10.1080/1350486X.2020.1779597
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    Cited by:

    1. Peter Carr & Lorenzo Torricelli, 2021. "Additive logistic processes in option pricing," Finance and Stochastics, Springer, vol. 25(4), pages 689-724, October.
    2. Michele Azzone & Roberto Baviera, 2023. "Is (independent) subordination relevant in option pricing?," Papers 2307.08628, arXiv.org, revised Oct 2023.
    3. Chun Yat Yeung & Ali Hirsa, 2022. "Saddle-Point Approach to Large-Time Volatility Smile," Papers 2212.05671, arXiv.org.
    4. 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.
    5. Victor Korolev & Alexander Zeifman, 2023. "Quasi-Exponentiated Normal Distributions: Mixture Representations and Asymmetrization," Mathematics, MDPI, vol. 11(17), pages 1-14, September.

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