%0 Journal Article
%@ 0377-2217
%A Phelan, CE
%A Marazzina, D
%A Fusai, G
%A Germano, G
%D 2018
%F discovery:10063605
%I ELSEVIER SCIENCE BV
%J European Journal of Operational Research
%K Option pricing, Finance, Wiener–Hopf factorisation, Hilbert transform, Laplace transform, Spectral filter
%N 1
%P 210-223
%T Fluctuation identities with continuous monitoring and their application to the pricing of barrier options
%U https://discovery.ucl.ac.uk/id/eprint/10063605/
%V 271
%X 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.
%Z 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/).