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Fluctuation identities with continuous monitoring and their application to the pricing of barrier options

Phelan, CE; Marazzina, D; Fusai, G; Germano, G; (2018) Fluctuation identities with continuous monitoring and their application to the pricing of barrier options. European Journal of Operational Research , 271 (1) pp. 210-223. 10.1016/j.ejor.2018.04.016. Green open access

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Abstract

We present a numerical scheme to calculate fluctuation identities for exponential Lévy processes in the continuous monitoring case. This includes the Spitzer identities for touching a single upper or lower barrier, and the more difficult case of the two-barriers exit problem. These identities are given in the Fourier-Laplace domain and require numerical inverse transforms. Thus we cover a gap in the literature that has mainly studied the discrete monitoring case; indeed, there are no existing numerical methods that deal with the continuous case. As a motivating application we price continuously monitored barrier options with the underlying asset modelled by an exponential Lévy process. We perform a detailed error analysis of the method and develop error bounds to show how the performance is limited by the truncation error of the sinc-based fast Hilbert transform used for the Wiener–Hopf factorisation. By comparing the results for our new technique with those for the discretely monitored case (which is in the Fourier-z domain) as the monitoring time step approaches zero, we show that the error convergence with continuous monitoring represents a limit for the discretely monitored scheme.

Type: Article
Title: Fluctuation identities with continuous monitoring and their application to the pricing of barrier options
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.ejor.2018.04.016
Publisher version: https://doi.org/10.1016/j.ejor.2018.04.016
Language: English
Additional information: Copyright © 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license. (http://creativecommons.org/licenses/by/4.0/).
Keywords: Option pricing, Finance, Wiener–Hopf factorisation, Hilbert transform, Laplace transform, Spectral filter
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10063605
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