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Fluctuation identities with continuous monitoring and their application to price barrier options

Phelan, Carolyn E., Marazzina, Daniele, Fusai, Gianluca and Germano, Guido (2018) Fluctuation identities with continuous monitoring and their application to price barrier options. European Journal of Operational Research, 271 (1). pp. 210-223. ISSN 0377-2217

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Identification Number: 10.1016/j.ejor.2018.04.016


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.

Item Type: Article
Official URL:
Additional Information: © 2018 Elsevier B.V.
Divisions: Systemic Risk Centre
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Date Deposited: 26 Apr 2018 10:54
Last Modified: 15 May 2024 23:15
Projects: ES/K002309/1, 1482817
Funders: Economic and Social Research Council, Engineering and Physical Sciences Research Council

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