Super-hedging American Options with Semi-static Trading Strategies under Model Uncertainty · arXivDesk
1604.04608Apr 15, 2016Final version. To appear in the International Journal of Theoretical and Applied Finance. Keywords: American options, super-hedging, model uncertainty, semi-static trading strategies, randomized models
Super-hedging American Options with Semi-static Trading Strategies under Model Uncertainty
We consider the super-hedging price of an American option in a discrete-time market in which stocks are available for dynamic trading and European options are available for static trading. We show that the super-hedging price π is given by the supremum over the prices of the American option under randomized models. That is, π=sup(ci,Qi)i∑iciφQi
Nearby in the stack
, where
ci∈R+
and the martingale measure
Qi
are chosen such that
∑ici=1
and
∑iciQi
prices the European options correctly, and
φQi
is the price of the American option under the model
Qi
. Our result generalizes the example given in ArXiv:1604.02274 that the highest model based price can be considered as a randomization over models.