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Self-decomposability and option pricing

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  • Yor, Marc
  • Madan, Dilip B.
  • Carr, Peter
  • Geman, Hélyette
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    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 610 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.

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    Bibliographic Info

    Paper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/1380.

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    Date of creation: Jan 2007
    Date of revision:
    Publication status: Published in Mathematical Finance, 2007, Vol. 17, no. 1. pp. 31-57.Length: 26 pages
    Handle: RePEc:dau:papers:123456789/1380

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    Related research

    Keywords: Option pricing; Ornstein–Uhlenbeck Processes; Background Driving Lévy Processes; Scaling; Additive Processes;

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    Cited by:
    1. Bakshi, Gurdip & Panayotov, George, 2010. "First-passage probability, jump models, and intra-horizon risk," Journal of Financial Economics, Elsevier, vol. 95(1), pages 20-40, January.
    2. Johannes Siven & Rolf Poulsen, 2009. "Auto-static for the people: risk-minimizing hedges of barrier options," Review of Derivatives Research, Springer, vol. 12(3), pages 193-211, October.
    3. Finlay, Richard & Seneta, Eugene, 2012. "A Generalized Hyperbolic model for a risky asset with dependence," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2164-2169.
    4. Mathias Trabs, 2011. "Calibration of selfdecomposable Lévy models," SFB 649 Discussion Papers SFB649DP2011-073, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Fabozzi, Frank J. & Leccadito, Arturo & Tunaru, Radu S., 2014. "Extracting market information from equity options with exponential Lévy processes," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 125-141.
    6. N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
    7. Madan, Dilip B. & Schoutens, Wim, 2013. "Systemic risk tradeoffs and option prices," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 222-230.
    8. Michele Leonardo Bianchi, 2012. "An empirical comparison of alternative credit default swap pricing models," Temi di discussione (Economic working papers) 882, Bank of Italy, Economic Research and International Relations Area.

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