{"title":"Market information of the fractional stochastic regularity model","authors":"Daniele Angelini, Matthieu Garcin","doi":"arxiv-2409.07159","DOIUrl":null,"url":null,"abstract":"The Fractional Stochastic Regularity Model (FSRM) is an extension of\nBlack-Scholes model describing the multifractal nature of prices. It is based\non a multifractional process with a random Hurst exponent $H_t$, driven by a\nfractional Ornstein-Uhlenbeck (fOU) process. When the regularity parameter\n$H_t$ is equal to $1/2$, the efficient market hypothesis holds, but when\n$H_t\\neq 1/2$ past price returns contain some information on a future trend or\nmean-reversion of the log-price process. In this paper, we investigate some\nproperties of the fOU process and, thanks to information theory and Shannon's\nentropy, we determine theoretically the serial information of the regularity\nprocess $H_t$ of the FSRM, giving some insight into one's ability to forecast\nfuture price increments and to build statistical arbitrages with this model.","PeriodicalId":501139,"journal":{"name":"arXiv - QuantFin - Statistical Finance","volume":"34 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - QuantFin - Statistical Finance","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.07159","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
The Fractional Stochastic Regularity Model (FSRM) is an extension of
Black-Scholes model describing the multifractal nature of prices. It is based
on a multifractional process with a random Hurst exponent $H_t$, driven by a
fractional Ornstein-Uhlenbeck (fOU) process. When the regularity parameter
$H_t$ is equal to $1/2$, the efficient market hypothesis holds, but when
$H_t\neq 1/2$ past price returns contain some information on a future trend or
mean-reversion of the log-price process. In this paper, we investigate some
properties of the fOU process and, thanks to information theory and Shannon's
entropy, we determine theoretically the serial information of the regularity
process $H_t$ of the FSRM, giving some insight into one's ability to forecast
future price increments and to build statistical arbitrages with this model.