Algorithms of Finite Difference for Pricing American Options under Fractional Diffusion Models
Joint Authors
Xi, Jun
Chen, Yanqing
Cao, Jianwen
Source
Mathematical Problems in Engineering
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-09-30
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
It is well known that linear complementarity problem (LCP) involving partial integro differential equation (PIDE) arises from pricing American options under Lévy Models.
In the case of infinite activity process, the integral part of the PIDE has a singularity, which is generally approximated by a small Brownian component plus a compound Poisson process, in the neighborhood of origin.
The PIDE can be reformulated as a fractional partial differential equation (FPDE) under fractional diffusion models, including FMLS (finite moment log stable), CGMY (Carr-Madan-Geman-Yor), and KoBol (Koponen-Boyarchenko-Levendorskii).
In this paper, we first present a stable iterative algorithm, which is based on the fractional difference approach and penalty method, to avoid the singularity problem and obtain numerical approximations of first-order accuracy.
Then, on the basis of the first-order accurate algorithm, spatial extrapolation is employed to obtain second-order accurate numerical estimates.
Numerical tests are performed to demonstrate the effectiveness of the algorithm and the extrapolation method.
We believe thatthis can be used as necessary tools by the engineers in research.
American Psychological Association (APA)
Xi, Jun& Chen, Yanqing& Cao, Jianwen. 2014. Algorithms of Finite Difference for Pricing American Options under Fractional Diffusion Models. Mathematical Problems in Engineering،Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-1044197
Modern Language Association (MLA)
Xi, Jun…[et al.]. Algorithms of Finite Difference for Pricing American Options under Fractional Diffusion Models. Mathematical Problems in Engineering No. 2014 (2014), pp.1-8.
https://search.emarefa.net/detail/BIM-1044197
American Medical Association (AMA)
Xi, Jun& Chen, Yanqing& Cao, Jianwen. Algorithms of Finite Difference for Pricing American Options under Fractional Diffusion Models. Mathematical Problems in Engineering. 2014. Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-1044197
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1044197