Reconstruction of the local volatility function using the Black–Scholes model
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Kim, S. | - |
dc.contributor.author | Han, H. | - |
dc.contributor.author | Jang, H. | - |
dc.contributor.author | Jeong, D. | - |
dc.contributor.author | Lee, C. | - |
dc.contributor.author | Lee, W. | - |
dc.contributor.author | Kim, J. | - |
dc.date.accessioned | 2021-12-03T00:41:32Z | - |
dc.date.available | 2021-12-03T00:41:32Z | - |
dc.date.created | 2021-08-31 | - |
dc.date.issued | 2021-04 | - |
dc.identifier.issn | 1877-7503 | - |
dc.identifier.uri | https://scholar.korea.ac.kr/handle/2021.sw.korea/129000 | - |
dc.description.abstract | In this paper, we propose a robust and accurate numerical algorithm to reconstruct a local volatility function using the Black–Scholes (BS) partial differential equation (PDE). Using the BS PDE and given market data, option prices at strike prices and expiry times, a time-dependent local volatility function is computed. The proposed algorithm consists of the following steps: (1) The time-dependent volatility function is computed using a recently developed method; (2) A Monte Carlo simulation technique is used to find the effective region which has a strong influence on option prices; and we partition the effective domain into several sub-regions and define a local volatility function based on the time-dependent volatility function on the sub-regions; and (3) Finally, we calibrate the local volatility function using the fully implicit finite difference method and the conjugate gradient optimization algorithm. We demonstrate the robustness and accuracy of the proposed local volatility reconstruction algorithm using manufactured volatility surface and real market data. © 2021 Elsevier B.V. | - |
dc.language | English | - |
dc.language.iso | en | - |
dc.publisher | Elsevier B.V. | - |
dc.subject | Commerce | - |
dc.subject | Conjugate gradient method | - |
dc.subject | Costs | - |
dc.subject | Finite difference method | - |
dc.subject | Accurate numerical algorithms | - |
dc.subject | Conjugate gradient optimization | - |
dc.subject | Effective domains | - |
dc.subject | Fully implicit finite differences | - |
dc.subject | Monte carlo simulation technique | - |
dc.subject | Partial differential equations (PDE) | - |
dc.subject | Reconstruction algorithms | - |
dc.subject | Time-dependent volatility function | - |
dc.subject | Monte Carlo methods | - |
dc.title | Reconstruction of the local volatility function using the Black–Scholes model | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Kim, J. | - |
dc.identifier.doi | 10.1016/j.jocs.2021.101341 | - |
dc.identifier.scopusid | 2-s2.0-85102292911 | - |
dc.identifier.wosid | 000649742800004 | - |
dc.identifier.bibliographicCitation | Journal of Computational Science, v.51 | - |
dc.relation.isPartOf | Journal of Computational Science | - |
dc.citation.title | Journal of Computational Science | - |
dc.citation.volume | 51 | - |
dc.type.rims | ART | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Computer Science | - |
dc.relation.journalWebOfScienceCategory | Computer Science, Interdisciplinary Applications | - |
dc.relation.journalWebOfScienceCategory | Computer Science, Theory & Methods | - |
dc.subject.keywordPlus | Commerce | - |
dc.subject.keywordPlus | Conjugate gradient method | - |
dc.subject.keywordPlus | Costs | - |
dc.subject.keywordPlus | Finite difference method | - |
dc.subject.keywordPlus | Accurate numerical algorithms | - |
dc.subject.keywordPlus | Conjugate gradient optimization | - |
dc.subject.keywordPlus | Effective domains | - |
dc.subject.keywordPlus | Fully implicit finite differences | - |
dc.subject.keywordPlus | Monte carlo simulation technique | - |
dc.subject.keywordPlus | Partial differential equations (PDE) | - |
dc.subject.keywordPlus | Reconstruction algorithms | - |
dc.subject.keywordPlus | Time-dependent volatility function | - |
dc.subject.keywordPlus | Monte Carlo methods | - |
dc.subject.keywordAuthor | Black–Scholes equation | - |
dc.subject.keywordAuthor | Finite difference method | - |
dc.subject.keywordAuthor | Local volatility | - |
dc.subject.keywordAuthor | Monte Carlo simulation | - |
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