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On Hedging American Options Under Model Uncertainty

20 Pages Posted: 27 Jan 2014  

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Yu-Jui Huang

University of Colorado at Boulder - Department of Applied Mathematics

Zhou Zhou

University of Minnesota - Twin Cities

Date Written: December 1, 2013

Abstract

We consider as given a discrete time financial market with a risky asset and options written on that asset and determine both the sub- and super-hedging prices of an American option in the model independent framework of ArXiv:1305.6008. We obtain the duality of results for the sub- and super-hedging prices. For the sub-hedging prices we discuss whether the sup and inf in the dual representation can be exchanged (a counter example shows that this is not true in general). For the super-hedging prices we discuss several alternative definitions and argue why our choice is more reasonable. Then assuming that the path space is compact, we construct a discretization of the path space and demonstrate the convergence of the hedging prices at the optimal rate. The latter result would be useful for numerical computation of the hedging prices. Our results generalize those of ArXiv:1304.3574 to the case when static positions in (finitely many) European options can be used in the hedging portfolio.

Keywords: American options, model independent pricing, semi-static hedging strategies

Suggested Citation

Bayraktar, Erhan and Huang, Yu-Jui and Zhou, Zhou, On Hedging American Options Under Model Uncertainty (December 1, 2013). Available at SSRN: https://ssrn.com/abstract=2385069 or http://dx.doi.org/10.2139/ssrn.2385069

Erhan Bayraktar (Contact Author)

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Yu-Jui Huang

University of Colorado at Boulder - Department of Applied Mathematics ( email )

Boulder, CO 80309
United States

HOME PAGE: http://www.yujui-huang.com

Zhou Zhou

University of Minnesota - Twin Cities ( email )

420 Delaware St. SE
Minneapolis, MN 55455
United States

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