Stochastic finite differences and multilevel Monte Carlo for a class of SPDEs in finance
In this article, we propose a Milstein finite difference scheme for a stochastic partial differential equation (SPDE) describing a large particle system. We show, by means of Fourier analysis, that the discretisation on an unbounded domain is convergent of first order in time and second order in the...
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| Format: | Report |
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2011
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| _version_ | 1797087904401457152 |
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| author | Reisinger, C Giles, M |
| author_facet | Reisinger, C Giles, M |
| author_sort | Reisinger, C |
| collection | OXFORD |
| description | In this article, we propose a Milstein finite difference scheme for a stochastic partial differential equation (SPDE) describing a large particle system. We show, by means of Fourier analysis, that the discretisation on an unbounded domain is convergent of first order in time and second order in the spatial grid size, and that the discretisation is stable with respect to boundary data. Numerical experiments clearly indicate that the same convergence order also holds for boundary-value problems. Multilevel path simulation, previously used for SDEs, is shown to give substantial complexity gains compared to a standard discretisation of the SPDE or direct simulation of the particle system. We derive complexity bounds and illustrate the results by an application to basket credit derivatives. |
| first_indexed | 2024-03-07T02:42:11Z |
| format | Report |
| id | oxford-uuid:aad613ee-30de-4e36-9187-c042d6027cf0 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T02:42:11Z |
| publishDate | 2011 |
| publisher | N/A |
| record_format | dspace |
| spelling | oxford-uuid:aad613ee-30de-4e36-9187-c042d6027cf02022-03-27T03:17:43ZStochastic finite differences and multilevel Monte Carlo for a class of SPDEs in financeReporthttp://purl.org/coar/resource_type/c_93fcuuid:aad613ee-30de-4e36-9187-c042d6027cf0Mathematical Institute - ePrintsN/A2011Reisinger, CGiles, MIn this article, we propose a Milstein finite difference scheme for a stochastic partial differential equation (SPDE) describing a large particle system. We show, by means of Fourier analysis, that the discretisation on an unbounded domain is convergent of first order in time and second order in the spatial grid size, and that the discretisation is stable with respect to boundary data. Numerical experiments clearly indicate that the same convergence order also holds for boundary-value problems. Multilevel path simulation, previously used for SDEs, is shown to give substantial complexity gains compared to a standard discretisation of the SPDE or direct simulation of the particle system. We derive complexity bounds and illustrate the results by an application to basket credit derivatives. |
| spellingShingle | Reisinger, C Giles, M Stochastic finite differences and multilevel Monte Carlo for a class of SPDEs in finance |
| title | Stochastic finite differences and multilevel Monte Carlo for a class of SPDEs in finance |
| title_full | Stochastic finite differences and multilevel Monte Carlo for a class of SPDEs in finance |
| title_fullStr | Stochastic finite differences and multilevel Monte Carlo for a class of SPDEs in finance |
| title_full_unstemmed | Stochastic finite differences and multilevel Monte Carlo for a class of SPDEs in finance |
| title_short | Stochastic finite differences and multilevel Monte Carlo for a class of SPDEs in finance |
| title_sort | stochastic finite differences and multilevel monte carlo for a class of spdes in finance |
| work_keys_str_mv | AT reisingerc stochasticfinitedifferencesandmultilevelmontecarloforaclassofspdesinfinance AT gilesm stochasticfinitedifferencesandmultilevelmontecarloforaclassofspdesinfinance |