Static and semistatic hedging as contrarian or conformist bets

Svetlana Boyarchenko and Sergei Levendorskiĭ

Mathematical Finance, 2020, vol. 30, issue 3, 921-960

Abstract: In this paper, we argue that, once the costs of maintaining the hedging portfolio are properly taken into account, semistatic portfolios should more properly be thought of as separate classes of derivatives, with nontrivial, model‐dependent payoff structures. We derive new integral representations for payoffs of exotic European options in terms of payoffs of vanillas, different from the Carr–Madan representation, and suggest approximations of the idealized static hedging/replicating portfolio using vanillas available in the market. We study the dependence of the hedging error on a model used for pricing and show that the variance of the hedging errors of static hedging portfolios can be sizably larger than the errors of variance‐minimizing portfolios. We explain why the exact semistatic hedging of barrier options is impossible for processes with jumps, and derive general formulas for variance‐minimizing semistatic portfolios. We show that hedging using vanillas only leads to larger errors than hedging using vanillas and first touch digitals. In all cases, efficient calculations of the weights of the hedging portfolios are in the dual space using new efficient numerical methods for calculation of the Wiener–Hopf factors and Laplace–Fourier inversion.

Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (13)

Downloads: (external link)
https://doi.org/10.1111/mafi.12240

Related works:
Working Paper: Static and semi-static hedging as contrarian or conformist bets (2019)
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:bla:mathfi:v:30:y:2020:i:3:p:921-960

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0960-1627

Access Statistics for this article

Mathematical Finance is currently edited by Jerome Detemple

More articles in Mathematical Finance from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().