A power penalty method for a 2D fractional partial differential linear complementarity problem governing two-asset American option pricing

Wen Chen and Song Wang

Applied Mathematics and Computation, 2017, vol. 305, issue C, 174-187

Abstract: In this paper we propose a power penalty method for a linear complementarity problem (LCP) involving a fractional partial differential operator in two spatial dimensions arising in pricing American options on two underlying assets whose prices follow two independent geometric Lévy processes. We first approximate the LCP by a nonlinear 2D fractional partial differential equation (fPDE) with a penalty term. We then prove that the solution to the fPDE converges to that of the LCP in a Sobolev norm at an exponential rate depending on the parameters used in the penalty term. The 2D fPDE is discretized by a 2nd-order finite difference method in space and Crank–Nicolson method in time. Numerical experiments on a model Basket Option pricing problem were performed to demonstrate the convergent rates and the effectiveness of the penalty method.

Keywords: American option pricing; Optimal control; Linear complementarity problem; Fractional differential equation; Penalty method; Finite difference method (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300317300954
Full text for ScienceDirect subscribers only

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:eee:apmaco:v:305:y:2017:i:c:p:174-187

DOI: 10.1016/j.amc.2017.01.069

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().