2016/04/15 by Erhan Bayraktar, Zhou Zhou, Bayraktar, Erhan +1 · 2 citations
Economics, Econometrics and Finance · Mathematics · #Capital Investment and Risk Analysis #FOS: Economics and business #FOS: Mathematics #Market Dynamics and Volatility #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Stochastic processes and financial applications #math.PR #q-fin.MF
paper · pdf · doi:10.48550/arxiv.1604.04608
Final 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
openalex publication_date 2016/04/15 · arxiv created 2017/06/26 · arxiv updated 2017/06/28 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
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, where ci ∈ ℝ+ and the martingale measure Qi are chosen such that ∑i ci=1 and ∑i ciQi 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.