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An analytical approximation for single barrier options under stochastic volatility models

Hideharu Funahashi () and Tomohide Higuchi ()
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Hideharu Funahashi: Mizuho Securities Co. Ltd.
Tomohide Higuchi: Mizuho Securities Co. Ltd.

Annals of Operations Research, 2018, vol. 266, issue 1, 129-157

Abstract: Abstract The aim of this paper is to derive an approximation formula for a single barrier option under local volatility models, stochastic volatility models, and their hybrids, which are widely used in practice. The basic idea of our approximation is to mimic a target underlying asset process by a polynomial of the Wiener process. We then translate the problem of solving first hit probability of the asset process into that of a Wiener process whose distribution of passage time is known. Finally, utilizing the Girsanov’s theorem and the reflection principle, we show that single barrier option prices can be approximated in a closed-form. Furthermore, ample numerical examples will show the accuracy of our approximation is high enough for practical applications.

Keywords: Single barrier option; Analytical approximation; Local and stochastic volatility models; Wiener–Ito chaos expansion (search for similar items in EconPapers)
Date: 2018
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