A power penalty method for a 2D fractional partial differential linear complementarity problem governing two-asset American option pricing
© 2017 Elsevier Inc.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 Lév...
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| Format: | Journal Article |
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Elsevier Inc.
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/52000 |
| _version_ | 1848758818935144448 |
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| author | Chen, W. Wang, Song |
| author_facet | Chen, W. Wang, Song |
| author_sort | Chen, W. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | © 2017 Elsevier Inc.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. |
| first_indexed | 2025-11-14T09:50:02Z |
| format | Journal Article |
| id | curtin-20.500.11937-52000 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:50:02Z |
| publishDate | 2017 |
| publisher | Elsevier Inc. |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-520002017-09-13T15:38:23Z A power penalty method for a 2D fractional partial differential linear complementarity problem governing two-asset American option pricing Chen, W. Wang, Song © 2017 Elsevier Inc.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. 2017 Journal Article http://hdl.handle.net/20.500.11937/52000 10.1016/j.amc.2017.01.069 Elsevier Inc. restricted |
| spellingShingle | Chen, W. Wang, Song A power penalty method for a 2D fractional partial differential linear complementarity problem governing two-asset American option pricing |
| title | A power penalty method for a 2D fractional partial differential linear complementarity problem governing two-asset American option pricing |
| title_full | A power penalty method for a 2D fractional partial differential linear complementarity problem governing two-asset American option pricing |
| title_fullStr | A power penalty method for a 2D fractional partial differential linear complementarity problem governing two-asset American option pricing |
| title_full_unstemmed | A power penalty method for a 2D fractional partial differential linear complementarity problem governing two-asset American option pricing |
| title_short | A power penalty method for a 2D fractional partial differential linear complementarity problem governing two-asset American option pricing |
| title_sort | power penalty method for a 2d fractional partial differential linear complementarity problem governing two-asset american option pricing |
| url | http://hdl.handle.net/20.500.11937/52000 |