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

Carolyn E. Phelan, Daniele Marazzina, Gianluca Fusai and Guido Germano

European Journal of Operational Research, 2018, vol. 271, issue 1, 210-223

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.

Keywords: Option pricing; Finance; Wiener–Hopf factorisation; Hilbert transform; Laplace transform; Spectral filter (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (13)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:271:y:2018:i:1:p:210-223

DOI: 10.1016/j.ejor.2018.04.016

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