EconPapers    
Economics at your fingertips  
 

EFFICIENT EVALUATION OF DOUBLE-BARRIER OPTIONS

Svetlana Boyarchenko () and Sergei Levendorskiä¬
Additional contact information
Svetlana Boyarchenko: Department of Economics, University of Texas at Austin, 2225 Speedway Stop C3100, Austin, TX 78712-0301, USA
Sergei Levendorskiä¬: Calico Science Consulting, 2708 Bolton Street, Austin, TX 78748, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2024, vol. 27, issue 02, 1-42

Abstract: In the paper, we develop a very fast and accurate method for pricing double barrier options with continuous monitoring in wide classes of Lévy models; the calculations are in the dual space, and the Wiener–Hopf factorization is used. For wide regions in the parameter space, the precision of the order of 10−15 is achievable in seconds, and of the order of 10−9–10−8 — in fractions of a second. The Wiener–Hopf factors and repeated integrals in the pricing formulas are calculated using sinh-deformations of the lines of integration, the corresponding changes of variables and the simplified trapezoid rule. If the Bromwich integral is calculated using the Gaver–Wynn Rho acceleration instead of the sinh-acceleration, the CPU time is typically smaller but the precision is of the order of 10−9–10−6, at best. Explicit pricing algorithms and numerical examples are for no-touch options, digitals (equivalently, for the joint distribution function of a Lévy process and its supremum and infimum processes), and call options. Several graphs are produced to explain fundamental difficulties for accurate pricing of barrier options using time discretization and interpolation-based calculations in the state space.

Keywords: Lévy process; extrema of a Lévy process; double-barrier options; Fourier transform; Gaver–Wynn Rho algorithm; sinh-acceleration (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0219024924500079
Access to full text is restricted to subscribers

Related works:
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:wsi:ijtafx:v:27:y:2024:i:02:n:s0219024924500079

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0219024924500079

Access Statistics for this article

International Journal of Theoretical and Applied Finance (IJTAF) is currently edited by L P Hughston

More articles in International Journal of Theoretical and Applied Finance (IJTAF) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().

 
Page updated 2025-05-24
Handle: RePEc:wsi:ijtafx:v:27:y:2024:i:02:n:s0219024924500079