Finite Difference Methods for Option Pricing under Lévy Processes: Wiener-Hopf Factorization Approach
Author
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-10-09
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
In the paper, we consider the problem of pricing options in wide classes of Lévy processes.
We propose a general approach to the numerical methods based on a finite difference approximation for the generalized Black-Scholes equation.
The goal of the paper is to incorporate the Wiener-Hopf factorization into finite difference methods for pricing options in Lévy models with jumps.
The method is applicable for pricing barrier and American options.
The pricing problem is reduced to the sequence of linear algebraic systems with a dense Toeplitz matrix; then the Wiener-Hopf factorization method is applied.
We give an important probabilistic interpretation based on the infinitely divisible distributions theory to the Laurent operators in the correspondentfactorization identity.
Notice that our algorithm has the same complexity as the ones which use the explicit-implicit scheme, with a tridiagonal matrix.
However, our method is more accurate.
We support the advantage of the new method in terms of accuracy and convergence by using numerical experiments.
American Psychological Association (APA)
Kudryavtsev, Oleg. 2013. Finite Difference Methods for Option Pricing under Lévy Processes: Wiener-Hopf Factorization Approach. The Scientific World Journal،Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-1033499
Modern Language Association (MLA)
Kudryavtsev, Oleg. Finite Difference Methods for Option Pricing under Lévy Processes: Wiener-Hopf Factorization Approach. The Scientific World Journal No. 2013 (2013), pp.1-12.
https://search.emarefa.net/detail/BIM-1033499
American Medical Association (AMA)
Kudryavtsev, Oleg. Finite Difference Methods for Option Pricing under Lévy Processes: Wiener-Hopf Factorization Approach. The Scientific World Journal. 2013. Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-1033499
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1033499