In this technical note we provide a smoothed perturbation analysis (SPA) estimator of the sensitivity of a discrete time Parisian option with respect to the barrier level. The analysis put forward is of interest in a broader context than that of exotic options as we provide an SPA analysis for a problem where the critical event for the SPA estimator is based on an entire sample path, which is a novelty in the literature. Numerical examples illustrate the performance of the estimator.
Leahu, H., Heidergott, B. F., & Volk-Makarewicz, W. (2015). A smoothed perturbation analysis for Parisian options. IEEE Transactions on Automatic Control, 60(2), 469-474. https://doi.org/10.1109/TAC.2014.2326717