Abstract
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) |
---|---|
Article number | 1750036 |
Journal | International Journal of Theoretical and Applied Finance |
Volume | 20 |
Issue number | 6 |
DOIs | |
State | Published - Sep 1 2017 |
Bibliographical note
Publisher Copyright:© 2017 World Scientific Publishing Company.
Keywords
- American options
- model uncertainty
- randomized models
- semi-static trading strategies
- super-hedging