Matches in SemOpenAlex for { <https://semopenalex.org/work/W25673936> ?p ?o ?g. }
Showing items 1 to 83 of
83
with 100 items per page.
- W25673936 abstract "This thesis is concerned with the derivation, numerical analysis and implementation of high-order compact finite difference schemes for parabolic partial differential equations in multiple spatial dimensions. All those partial differential equations contain mixed derivative terms. The resulting schemes have been applied to equations appearing in computational finance.First, we develop and study essentially high-order compact finite difference schemes in a general setting with option pricing in stochastic volatility models on non-uniform grids as application. The schemes are fourth-order accurate in space and second-order accurate in time for vanishing correlation. In the numerical study we obtain high-order numerical convergence also for non-zero correlation and non-smooth payoffs which are typical in option pricing. In all numerical experiment a comparative standard second-order discretisation is significantly outperform. We conduct a numerical stability study which indicates unconditional stability of the scheme. Second, we derive and analyse high-order compact schemes with n-dimensional spatial domain in a general setting. We obtain fourth-order accuracy in space and second-order accuracy in time. A thorough von Newmann stability analysis is performed for spatial domain with dimensions two and three. We prove that a necessary stability condition holds unconditionally without additional restrictions on the choice of the discretisation parameters for vanishing mixed derivative terms. We also give partial results for non-vanishing mixed derivative terms. As first example Black-Scholes Basket options are considered. In all numerical experiments, where the initial conditions were smoothened using the smoothing operators developed by Kreiss, Thomee and Widlund, a comparative standard second-order discretisation is significantly outperformed. As second example the multi-dimentional Heston basket option is considered for n independent Heston processes, where for each Heston process there is a non-vanishing correlation between the stock and its volatility." @default.
- W25673936 created "2016-06-24" @default.
- W25673936 creator A5080957174 @default.
- W25673936 date "2014-08-30" @default.
- W25673936 modified "2023-09-23" @default.
- W25673936 title "High-order compact finite difference schemes for parabolic partial differential equations with mixed derivative terms and applications in computational finance" @default.
- W25673936 hasPublicationYear "2014" @default.
- W25673936 type Work @default.
- W25673936 sameAs 25673936 @default.
- W25673936 citedByCount "0" @default.
- W25673936 crossrefType "dissertation" @default.
- W25673936 hasAuthorship W25673936A5080957174 @default.
- W25673936 hasConcept C105795698 @default.
- W25673936 hasConcept C112972136 @default.
- W25673936 hasConcept C119857082 @default.
- W25673936 hasConcept C134306372 @default.
- W25673936 hasConcept C136798861 @default.
- W25673936 hasConcept C176321772 @default.
- W25673936 hasConcept C181330731 @default.
- W25673936 hasConcept C186219872 @default.
- W25673936 hasConcept C205951836 @default.
- W25673936 hasConcept C2780829570 @default.
- W25673936 hasConcept C28826006 @default.
- W25673936 hasConcept C33923547 @default.
- W25673936 hasConcept C3770464 @default.
- W25673936 hasConcept C39177556 @default.
- W25673936 hasConcept C41008148 @default.
- W25673936 hasConcept C48753275 @default.
- W25673936 hasConcept C51544822 @default.
- W25673936 hasConcept C53846429 @default.
- W25673936 hasConcept C73000952 @default.
- W25673936 hasConcept C78045399 @default.
- W25673936 hasConcept C93779851 @default.
- W25673936 hasConcept C97826883 @default.
- W25673936 hasConceptScore W25673936C105795698 @default.
- W25673936 hasConceptScore W25673936C112972136 @default.
- W25673936 hasConceptScore W25673936C119857082 @default.
- W25673936 hasConceptScore W25673936C134306372 @default.
- W25673936 hasConceptScore W25673936C136798861 @default.
- W25673936 hasConceptScore W25673936C176321772 @default.
- W25673936 hasConceptScore W25673936C181330731 @default.
- W25673936 hasConceptScore W25673936C186219872 @default.
- W25673936 hasConceptScore W25673936C205951836 @default.
- W25673936 hasConceptScore W25673936C2780829570 @default.
- W25673936 hasConceptScore W25673936C28826006 @default.
- W25673936 hasConceptScore W25673936C33923547 @default.
- W25673936 hasConceptScore W25673936C3770464 @default.
- W25673936 hasConceptScore W25673936C39177556 @default.
- W25673936 hasConceptScore W25673936C41008148 @default.
- W25673936 hasConceptScore W25673936C48753275 @default.
- W25673936 hasConceptScore W25673936C51544822 @default.
- W25673936 hasConceptScore W25673936C53846429 @default.
- W25673936 hasConceptScore W25673936C73000952 @default.
- W25673936 hasConceptScore W25673936C78045399 @default.
- W25673936 hasConceptScore W25673936C93779851 @default.
- W25673936 hasConceptScore W25673936C97826883 @default.
- W25673936 hasLocation W256739361 @default.
- W25673936 hasOpenAccess W25673936 @default.
- W25673936 hasPrimaryLocation W256739361 @default.
- W25673936 hasRelatedWork W1576381313 @default.
- W25673936 hasRelatedWork W1745672195 @default.
- W25673936 hasRelatedWork W2049599235 @default.
- W25673936 hasRelatedWork W2056904743 @default.
- W25673936 hasRelatedWork W2086754590 @default.
- W25673936 hasRelatedWork W2198826055 @default.
- W25673936 hasRelatedWork W2296685868 @default.
- W25673936 hasRelatedWork W2368861806 @default.
- W25673936 hasRelatedWork W2533010719 @default.
- W25673936 hasRelatedWork W2770640374 @default.
- W25673936 hasRelatedWork W2801020567 @default.
- W25673936 hasRelatedWork W2950581870 @default.
- W25673936 hasRelatedWork W2964080327 @default.
- W25673936 hasRelatedWork W3121209513 @default.
- W25673936 hasRelatedWork W3122428288 @default.
- W25673936 hasRelatedWork W3124833229 @default.
- W25673936 hasRelatedWork W3151491349 @default.
- W25673936 hasRelatedWork W3186500556 @default.
- W25673936 hasRelatedWork W3200641885 @default.
- W25673936 hasRelatedWork W590921569 @default.
- W25673936 isParatext "false" @default.
- W25673936 isRetracted "false" @default.
- W25673936 magId "25673936" @default.
- W25673936 workType "dissertation" @default.