NDLI: On Hedging American Options under Model Uncertainty

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Zhou, Zhou Huang, Yu-Jui Bayraktar, Erhan
Copyright Year	2015
Abstract	We consider as given a discrete time financial market with a risky asset and options written on that asset, and we determine both the sub- and superhedging prices of an American option in the model independent framework of [B. Bouchard and M. Nutz, Ann. Appl. Probab., 25 (2015), pp. 823--859]. We obtain the duality of results for the sub- and superhedging prices, as well as the existence of optimal hedging strategies. For the subhedging prices we discuss whether the sup and inf in the dual representation can be exchanged (a counterexample shows that this is not true in general). For the superhedging prices we discuss several alternative definitions and argue that 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 [Y. Dolinsky, Electron. Commun. Probab., 19 (2014), 19] to the case when static positions in (finitely many) European options can be used in the hedging portfolio.
Starting Page	425
Ending Page	447
Page Count	23
File Format	PDF
DOI	10.1137/140961869
e-ISSN	1945497X
Journal	SIAM Journal on Financial Mathematics (SJFMBJ)
Issue Number	1
Volume Number	6
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2015-06-16
Access Restriction	Subscribed
Subject Keyword	semistatic hedging strategies Dynamic programming method Optimal stochastic control American options Stopping times; optimal stopping problems; gambling theory Martingales with discrete parameter model independent pricing
Content Type	Text
Resource Type	Article

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