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

Phelan, C. E., Marazzina, D., Fusai, G. ORCID: 0000-0001-9215-2586 & 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. doi: 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.

Publication Type: Article
Additional Information: © 2018, Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Publisher Keywords: Option pricing, Finance, Wiener–Hopf factorisation, Hilbert transform, Laplace transform, Spectral filter
Subjects: H Social Sciences > HG Finance
Departments: Bayes Business School > Finance
Text - Accepted Version
Available under License Creative Commons Attribution Non-commercial No Derivatives.

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