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Self‐Decomposability And Option Pricing

Author

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  • Peter Carr
  • Hélyette Geman
  • Dilip B. Madan
  • Marc Yor

Abstract

The risk‐neutral process is modeled by a four parameter self‐similar process of independent increments with a self‐decomposable law for its unit time distribution. Six different processes in this general class are theoretically formulated and empirically investigated. We show that all six models are capable of adequately synthesizing European option prices across the spectrum of strikes and maturities at a point of time. Considerations of parameter stability over time suggest a preference for two of these models. Currently, there are several option pricing models with 6–10 free parameters that deliver a comparable level of performance in synthesizing option prices. The dimension reduction attained here should prove useful in studying the variation over time of option prices.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:mathfi:v:17:y:2007:i:1:p:31-57
    DOI: 10.1111/j.1467-9965.2007.00293.x
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    Cited by:

    1. 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.
    2. P. Peirano & D. Challet, 2012. "Baldovin-Stella stochastic volatility process and Wiener process mixtures," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 85(8), pages 1-12, August.
    3. Albrecher, Hansjoerg & Guillaume, Florence & Schoutens, Wim, 2013. "Implied liquidity: Model sensitivity," Journal of Empirical Finance, Elsevier, vol. 23(C), pages 48-67.
    4. Zorana Grbac & David Krief & Peter Tankov, 2015. "Approximate Option Pricing in the L\'evy Libor Model," Papers 1511.08466, arXiv.org, revised Jul 2016.
    5. Dilip B. Madan & Wim Schoutens, 2019. "Equilibrium Asset Returns In Financial Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 1-43, March.
    6. Dilip B. Madan & Wim Schoutens, 2019. "Conic asset pricing and the costs of price fluctuations," Annals of Finance, Springer, vol. 15(1), pages 29-58, March.
    7. Marina Marena & Andrea Romeo & Patrizia Semeraro, 2018. "Multivariate Factor-Based Processes With Sato Margins," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-30, February.
    8. Dilip B. Madan, 2016. "Risk premia in option markets," Annals of Finance, Springer, vol. 12(1), pages 71-94, February.
    9. Ballotta, Laura & Rayée, Grégory, 2022. "Smiles & smirks: Volatility and leverage by jumps," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1145-1161.
    10. Patrizia Semeraro, 2021. "Multivariate tempered stable additive subordination for financial models," Papers 2105.00844, arXiv.org, revised Sep 2021.
    11. Shantanu Awasthi & Indranil SenGupta, 2020. "First exit-time analysis for an approximate Barndorff-Nielsen and Shephard model with stationary self-decomposable variance process," Papers 2006.07167, arXiv.org, revised Jan 2021.
    12. Weilong Fu & Ali Hirsa, 2019. "A fast method for pricing American options under the variance gamma model," Papers 1903.07519, arXiv.org.
    13. Boris Buchmann & Kevin W. Lu & Dilip B. Madan, 2019. "Calibration for Weak Variance-Alpha-Gamma Processes," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1151-1164, December.
    14. Dilip B. Madan, 2016. "Adapted hedging," Annals of Finance, Springer, vol. 12(3), pages 305-334, December.
    15. 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.
    16. Maejima, Makoto & Ueda, Yohei, 2010. "[alpha]-selfdecomposable distributions and related Ornstein-Uhlenbeck type processes," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2363-2389, December.
    17. Wang, Yiming & Tong, Hanfei, 2008. "Modeling and estimating the jump risk of exchange rates: Applications to RMB," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6575-6583.
    18. Florence Guillaume, 2018. "Multivariate Option Pricing Models With Lévy And Sato Vg Marginal Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-26, March.
    19. Boris Buchmann & Kevin W. Lu & Dilip B. Madan, 2018. "Calibration for Weak Variance-Alpha-Gamma Processes," Papers 1801.08852, arXiv.org, revised Jul 2018.
    20. Dilip Madan, 2011. "Joint risk-neutral laws and hedging," IISE Transactions, Taylor & Francis Journals, vol. 43(12), pages 840-850.
    21. Li, Jing & Li, Lingfei & Zhang, Gongqiu, 2017. "Pure jump models for pricing and hedging VIX derivatives," Journal of Economic Dynamics and Control, Elsevier, vol. 74(C), pages 28-55.
    22. Patrizia Semeraro, 2022. "Multivariate tempered stable additive subordination for financial models," Mathematics and Financial Economics, Springer, volume 16, number 3, March.
    23. Michele Bianchi & Frank Fabozzi, 2015. "Investigating the Performance of Non-Gaussian Stochastic Intensity Models in the Calibration of Credit Default Swap Spreads," Computational Economics, Springer;Society for Computational Economics, vol. 46(2), pages 243-273, August.
    24. Massimo Arnone & Michele Leonardo Bianchi & Anna Grazia Quaranta & Gian Luca Tassinari, 2021. "Catastrophic risks and the pricing of catastrophe equity put options," Computational Management Science, Springer, vol. 18(2), pages 213-237, June.
    25. Dilip B. Madan & King Wang, 2022. "Two sided efficient frontiers at multiple time horizons," Annals of Finance, Springer, vol. 18(3), pages 327-353, September.

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