Static and Semi-Static Hedging as Contrarian or Conformist Bets

65 Pages Posted: 14 Feb 2019

See all articles by Svetlana Boyarchenko

Svetlana Boyarchenko

University of Texas at Austin - Department of Economics

Sergei Levendorskii

Calico Science Consulting

Date Written: February 6, 2019

Abstract

In this paper, we argue that, once the costs of maintaining the hedging portfolio are properly taken into account, semi-static portfolios should more properly be thought of as separate classes of derivatives, with non-trivial, model-dependent payoff structures. We derive new integral representations for payoffs of exotic European options in terms of payoffs of vanillas, different from 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 sizeably larger than the errors of variance-minimizing portfolios. We explain why the exact semi-static hedging of barrier options is impossible for processes with jumps, and derive general formulas for variance-minimizing semi-static portfolio. 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.

Keywords: Static Hedging, Semi-Static Hedging, Levy Processes, Exotic European Options, Barrier Options, Wiener-Hopf Factorization, Fourier-Laplace Inversion, Sinh-Acceleration

JEL Classification: C02, C67, Z23

Suggested Citation

Boyarchenko, Svetlana I. and Levendorskii, Sergei Z., Static and Semi-Static Hedging as Contrarian or Conformist Bets (February 6, 2019). Available at SSRN: https://ssrn.com/abstract=3329694 or http://dx.doi.org/10.2139/ssrn.3329694

Svetlana I. Boyarchenko

University of Texas at Austin - Department of Economics ( email )

Austin, TX 78712
United States

Sergei Z. Levendorskii (Contact Author)

Calico Science Consulting ( email )

Austin, TX
United States

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