Adaptive Finite Element Solution of 1D European Option Pricing Problems
We present a piecewise Hermite cubic adaptive finite element method for solving a generalised European Black-Scholes problem to guaranteed accuracy. Specifically, we prove a residual-based a posteriori error bound in the $L^{2}(\Omega)$-norm, at contract issue, for a continuous Galerkin approximatio...
| Main Authors: | , |
|---|---|
| Format: | Report |
| Published: |
Unspecified
1997
|
| _version_ | 1826275430538149888 |
|---|---|
| author | Jackson, N Suli, E |
| author_facet | Jackson, N Suli, E |
| author_sort | Jackson, N |
| collection | OXFORD |
| description | We present a piecewise Hermite cubic adaptive finite element method for solving a generalised European Black-Scholes problem to guaranteed accuracy. Specifically, we prove a residual-based a posteriori error bound in the $L^{2}(\Omega)$-norm, at contract issue, for a continuous Galerkin approximation to the solution using Galerkin orthogonality and weighted strong stability of an associated dual problem. We use this bound to construct an adaptive algorithm to generate a space-time discretisation which ensures that the error norm is less than a given tolerance. We demonstrate the speed and accuracy of our method through example pricings. |
| first_indexed | 2024-03-06T22:58:35Z |
| format | Report |
| id | oxford-uuid:61481632-b94d-4b8d-a53d-594f456d23aa |
| institution | University of Oxford |
| last_indexed | 2024-03-06T22:58:35Z |
| publishDate | 1997 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:61481632-b94d-4b8d-a53d-594f456d23aa2022-03-26T17:58:51ZAdaptive Finite Element Solution of 1D European Option Pricing ProblemsReporthttp://purl.org/coar/resource_type/c_93fcuuid:61481632-b94d-4b8d-a53d-594f456d23aaMathematical Institute - ePrintsUnspecified1997Jackson, NSuli, EWe present a piecewise Hermite cubic adaptive finite element method for solving a generalised European Black-Scholes problem to guaranteed accuracy. Specifically, we prove a residual-based a posteriori error bound in the $L^{2}(\Omega)$-norm, at contract issue, for a continuous Galerkin approximation to the solution using Galerkin orthogonality and weighted strong stability of an associated dual problem. We use this bound to construct an adaptive algorithm to generate a space-time discretisation which ensures that the error norm is less than a given tolerance. We demonstrate the speed and accuracy of our method through example pricings. |
| spellingShingle | Jackson, N Suli, E Adaptive Finite Element Solution of 1D European Option Pricing Problems |
| title | Adaptive Finite Element Solution of 1D European Option Pricing Problems |
| title_full | Adaptive Finite Element Solution of 1D European Option Pricing Problems |
| title_fullStr | Adaptive Finite Element Solution of 1D European Option Pricing Problems |
| title_full_unstemmed | Adaptive Finite Element Solution of 1D European Option Pricing Problems |
| title_short | Adaptive Finite Element Solution of 1D European Option Pricing Problems |
| title_sort | adaptive finite element solution of 1d european option pricing problems |
| work_keys_str_mv | AT jacksonn adaptivefiniteelementsolutionof1deuropeanoptionpricingproblems AT sulie adaptivefiniteelementsolutionof1deuropeanoptionpricingproblems |