Bilateral multiple gamma returns: Their risks and rewards

Dilip B. Madan, Wim Schoutens () and King Wang ()
Additional contact information
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

International Journal of Financial Engineering (IJFE), 2020, vol. 07, issue 01, 1-27

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.

Keywords: Entropy maximization; variance gamma; distorted expectation; measure distortion; skewness premia (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
https://www.worldscientific.com/doi/abs/10.1142/S2424786320500085
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijfexx:v:07:y:2020:i:01:n:s2424786320500085

Ordering information: This journal article can be ordered from

DOI: 10.1142/S2424786320500085

Access Statistics for this article

International Journal of Financial Engineering (IJFE) is currently edited by George Yuan

More articles in International Journal of Financial Engineering (IJFE) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().