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Monte Carlo pathwise sensitivities for barrier options

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  • Thomas Gerstner
  • Bastian Harrach
  • 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 two-dimensional calibration of a CoCo-Bond, which we model with different types of discretely monitored barrier options.

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  • Thomas Gerstner & Bastian Harrach & Daniel Roth, 2018. "Monte Carlo pathwise sensitivities for barrier options," Papers 1804.03975, arXiv.org, revised Apr 2019.
    • Handle: RePEc:arx:papers:1804.03975
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    References listed on IDEAS

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    1. Paul Glasserman & Jeremy Staum, 2001. "Conditioning on One-Step Survival for Barrier Option Simulations," Operations Research, INFORMS, vol. 49(6), pages 923-937, December.
    2. Peter G Zhang, 1998. "Exotic Options:A Guide to Second Generation Options," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 3800.
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