Before revision: In this paper, we focus on model-free pricing and robust hedging of options depending on the local time , consistent with Vanilla options. This problem is classically approached by means of the Skorokhod embedding problem (SEP), which consists in representing a given probability on the real line as the distribution of a Brownian motion stopped at a chosen stopping time .
After revision: In this paper, we focus on model-free pricing and robust hedging of options depending on the local time when one or more marginals of the underlying price process are known .