Monte Carlo pathwise sensitivities for barrier options

Thomas Gerstner, Bastian Harrach and Daniel Roth

Journal of Computational Finance

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.

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