Robust Hedging of Options on Local Time.

Summary 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. By using the stochastic control approach initiated in Galichon, Henry-Labordere and Touzi, we recover the optimal hedging strategies and the corresponding prices given by Vallois' embeddings to the SEP. Furthermore, we extend the analysis to the two-marginal case. We provide a construction of two-marginal embedding and some examples for which the robust superhedging problem is solved. Finally, a special multi-marginal case is studied, where we construct a Markov martingale and compute its explicit generator. In particular, we provide a new example of fake Brownian motion.