Monte Carlo pathwise sensitivities for barrier options

TL;DR

This paper introduces a novel Monte Carlo algorithm capable of computing pathwise sensitivities for discontinuous payoff functions, enhancing the analysis of barrier options in financial modeling.

Contribution

It combines one-step survival and stable differentiation methods to enable sensitivity calculations for discontinuous payoffs, which was previously challenging.

Findings

Effective calculation of sensitivities for barrier options.

Application to calibrate CoCo-Bonds with discretely monitored barriers.

Improved accuracy in sensitivity analysis for discontinuous payoffs.

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.