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Bilateral multiple gamma returns: Their risks and rewards

Author

Listed:
  • Dilip B. Madan

    (Robert H. Smith School of Business, University of Maryland, College Park, MD 20742, USA)

  • Wim Schoutens

    (Department of Mathematics, Katholieke Universiteit Leuven, Leuven, Belgium)

  • King Wang

    (Derivative Product Strats, Morgan Stanley, 1585 Broadway, 5th Floor, New York, NY 10036, USA)

Abstract

The bilateral gamma model for returns is naturally derived from the lognormal model. Maximizing entropy in a random time change delivers the symmetric variance gamma model. The asymmetric variance gamma follows on incorporating skewness. Differential speeds for the upward and downward motions lead to the bilateral gamma. A further generalizations results in the bilateral double gamma model when the speed parameter of the bilateral gamma model is itself taken to be gamma distributed on entropy maximization. A rich five to seven parameter specification of preferences renders possible the extraction of physical densities from option prices. The quality of such extraction is measured by examining the uniformity of the estimated distribution functions evaluated at realized forward returns. The economic value of risky returns is seen to embed three/five risk premia for the bilateral gamma/bilateral double gamma. For the bilateral gamma they are up and down side volatilities compensated in up and down side drifts, and the down side drift compensated in the up side drift. For the bilateral double gamma one adds in addition compensations for skewness. Results reveal a drop in the down side risk premium since the crisis with an increase in the recent period.

Suggested Citation

  • Dilip B. Madan & Wim Schoutens & King Wang, 2020. "Bilateral multiple gamma returns: Their risks and rewards," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 1-27, March.
    • Handle: RePEc:wsi:ijfexx:v:07:y:2020:i:01:n:s2424786320500085
    DOI: 10.1142/S2424786320500085
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    References listed on IDEAS

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    3. Stephan Höcht & Dilip B. Madan & Wim Schoutens & Eva Verschueren, 2021. "It Takes Two to Tango: Estimation of the Zero-Risk Premium Strike of a Call Option via Joint Physical and Pricing Density Modeling," Risks, MDPI, vol. 9(11), pages 1-19, November.
    4. Yoshihiro Shirai, 2022. "Extreme Measures in Continuous Time Conic Finace," Papers 2210.13671, arXiv.org, revised Oct 2023.

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