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Is (independent) subordination relevant in option pricing?

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  • Michele Azzone
  • Roberto Baviera

Abstract

Monroe (1978) demonstrates that any local semimartingale can be represented as a time-changed Brownian Motion (BM). A natural question arises: does this representation theorem hold when the BM and the time-change are independent? We prove that a local semimartingale is not equivalent to a BM with a time-change that is independent from the BM. Our result is obtained utilizing a class of additive processes: the additive normal tempered stable (ATS). This class of processes exhibits an exceptional ability to accurately calibrate the equity volatility surface. We notice that the sub-class of additive processes that can be obtained with an independent additive subordination is incompatible with market data and shows significantly worse calibration performances than the ATS, especially on short time maturities. These results have been observed every business day in a semester on a dataset of S&P 500 and EURO STOXX 50 options.

Suggested Citation

  • Michele Azzone & Roberto Baviera, 2023. "Is (independent) subordination relevant in option pricing?," Papers 2307.08628, arXiv.org, revised Oct 2023.
    • Handle: RePEc:arx:papers:2307.08628
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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. 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.
    3. Peter Carr & Lorenzo Torricelli, 2021. "Additive logistic processes in option pricing," Finance and Stochastics, Springer, vol. 25(4), pages 689-724, October.
    4. 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.
    5. Azzone, Michele & Baviera, Roberto, 2021. "Synthetic forwards and cost of funding in the equity derivative market," Finance Research Letters, Elsevier, vol. 41(C).
    6. Thierry Ané & Hélyette Geman, 2000. "Order Flow, Transaction Clock, and Normality of Asset Returns," Journal of Finance, American Finance Association, vol. 55(5), pages 2259-2284, October.
    7. Ole E. Barndorff-Nielsen & Makoto Maejima & Ken-iti Sato, 2006. "Infinite Divisibility for Stochastic Processes and Time Change," Journal of Theoretical Probability, Springer, vol. 19(2), pages 411-446, June.
    8. 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.
    9. Hélyette Geman & Dilip B. Madan & Marc Yor, 2001. "Time Changes for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 79-96, January.
    10. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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