EconPapers    
Economics at your fingertips  
 

Spitzer identity, Wiener-Hopf factorization and pricing of discretely monitored exotic options

Gianluca Fusai, Guido Germano and Daniele Marazzina

European Journal of Operational Research, 2016, vol. 251, issue 1, 124-134

Abstract: The Wiener-Hopf factorization of a complex function arises in a variety of fields in applied mathematics such as probability, finance, insurance, queuing theory, radio engineering and fluid mechanics. The factorization fully characterizes the distribution of functionals of a random walk or a Lévy process, such as the maximum, the minimum and hitting times. Here we propose a constructive procedure for the computation of the Wiener-Hopf factors, valid for both single and double barriers, based on the combined use of the Hilbert and the z-transform. The numerical implementation can be simply performed via the fast Fourier transform and the Euler summation. Given that the information in the Wiener-Hopf factors is strictly related to the distributions of the first passage times, as a concrete application in mathematical finance we consider the pricing of discretely monitored exotic options, such as lookback and barrier options, when the underlying price evolves according to an exponential Lévy process. We show that the computational cost of our procedure is independent of the number of monitoring dates and the error decays exponentially with the number of grid points.

Keywords: Path-dependent options; Hilbert transform; Lévy process; Spitzer identity; Wiener-Hopf factorization (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (37)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0377221715010760
Full text for ScienceDirect subscribers only

Related works:
Working Paper: Spitzer identity, Wiener-Hopf factorization and pricing of discretely monitored exotic options (2016) Downloads
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:251:y:2016:i:1:p:124-134

DOI: 10.1016/j.ejor.2015.11.027

Access Statistics for this article

European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

More articles in European Journal of Operational Research from Elsevier
Bibliographic data for series maintained by Catherine Liu ().

 
Page updated 2025-03-23
Handle: RePEc:eee:ejores:v:251:y:2016:i:1:p:124-134