{"title":"Generalized measure Black-Scholes equation: Towards option self-similar pricing","authors":"Nizar Riane, Claire David","doi":"arxiv-2404.05214","DOIUrl":null,"url":null,"abstract":"In this work, we give a generalized formulation of the Black-Scholes model.\nThe novelty resides in considering the Black-Scholes model to be valid on\n'average', but such that the pointwise option price dynamics depends on a\nmeasure representing the investors' 'uncertainty'. We make use of the theory of\nnon-symmetric Dirichlet forms and the abstract theory of partial differential\nequations to establish well posedness of the problem. A detailed numerical\nanalysis is given in the case of self-similar measures.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"120 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - QuantFin - Mathematical Finance","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2404.05214","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this work, we give a generalized formulation of the Black-Scholes model.
The novelty resides in considering the Black-Scholes model to be valid on
'average', but such that the pointwise option price dynamics depends on a
measure representing the investors' 'uncertainty'. We make use of the theory of
non-symmetric Dirichlet forms and the abstract theory of partial differential
equations to establish well posedness of the problem. A detailed numerical
analysis is given in the case of self-similar measures.
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