Monte Carlo pathwise sensitivities for barrier options

Thomas Gerstner, Bastian Harrach and Daniel Roth

Abstract

The Monte Carlo pathwise sensitivities approach is well established for smooth payoff functions. In this work, we present a new Monte Carlo algorithm that is able to calculate the pathwise sensitivities for discontinuous payoff functions. Our main tool is to combine the one-step survival idea of Glasserman and Staum with the stable differentiation approach of Alm, Harrach, Harrach and Keller. As an application, we use the derived results for a five-dimensional calibration of a contingent convertible bond, which we model with different types of discretely monitored barrier options with time-dependent barrier levels.