| Title | A power penalty method for a 2D fractional partial differential linear complementarity problem governing two-asset American option pricing |
| Creator | |
| Date Issued | 2017-07-15 |
| Source Publication | Applied Mathematics and Computation
 |
| ISSN | 0096-3003 |
| Volume | 305Pages: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. |
| Keyword | American option pricing Finite difference method Fractional differential equation Linear complementarity problem Optimal control Penalty method |
| DOI | 10.1016/j.amc.2017.01.069 |
| URL | View source |
| Language | 英语English |
| Scopus ID | 2-s2.0-85013250206 |
| Citation statistics | |
| Document Type | Journal article |
| Identifier | http://repository.uic.edu.cn/handle/39GCC9TT/12715 |
| Collection | Research outside affiliated institution |
| Corresponding Author | Wang，Song |
| Affiliation | 1.CSIRO Data61,34 Village Street, Docklands, Vic,Australia 2.Department of Mathematics & Statistics,Curtin University,Perth,GPO Box U1987,Australia |
| Recommended Citation GB/T 7714 | Chen，Wen,Wang，Song. A power penalty method for a 2D fractional partial differential linear complementarity problem governing two-asset American option pricing[J]. Applied Mathematics and Computation, 2017, 305: 174-187. |
| APA | Chen，Wen, & Wang，Song. (2017). A power penalty method for a 2D fractional partial differential linear complementarity problem governing two-asset American option pricing. Applied Mathematics and Computation, 305, 174-187. |
| MLA | Chen，Wen,et al."A power penalty method for a 2D fractional partial differential linear complementarity problem governing two-asset American option pricing". Applied Mathematics and Computation 305(2017): 174-187. |
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