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)iΣiciÏ•Qi, where ci ∈ R+ and the martingale measure Qi are chosen such that Σici = 1 and ΣiciQi prices the European options correctly, and Ï•Qi is the price of the American option under the model Qi. Our result generalizes the example given in Hobson & Neuberger (2016) that the highest model-based price can be considered as a randomization over models.
|Original language||English (US)|
|Journal||International Journal of Theoretical and Applied Finance|
|State||Published - Sep 1 2017|
Bibliographical noteFunding Information:
E. Bayraktar is supported in part by the National Science Foundation under grant DMS-1613170 and the Susan M. Smith chair.
- American options
- model uncertainty
- randomized models
- semi-static trading strategies