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On the optimal forecast with the fractional Brownian motion
Wang, Xiaohu1,2; Yu, Jun3; Zhang, Chen3
2024-01
Source PublicationQuantitative Finance
ABS Journal Level3
ISSN1469-7688
Volume24Issue:2Pages:337-346
Abstract

This paper investigates the performance of different forecasting formulas with fractional Brownian motion based on discrete and finite samples. Existing literature presents two formulas for generating optimal forecasts when continuous records are available. One formula relies on a history over an infinite past, while the other is designed for a record limited to a finite past. In reality, only observations at discrete time points over a finite past are available. In this case, the forecasting formula, which has been widely used in the literature, is the one obtained by Gatheral et al. (Volatility is rough. Quant. Finance, 2018, 18(6), 933–949) that truncates and discretizes the formula based on continuous records over an infinite past. The present paper advocates an alternative forecasting formula, which is the conditional expectation based on finite past discrete-time observations. The findings suggest that the conditional expectation approach produces more accurate forecasts than the existing method, as demonstrated by both simulated data and actual daily realized volatility (RV) observations. Moreover, we also provide empirical evidence showing that the conditional expectation approach can lead to larger economic values than the existing method.

KeywordConditional Expectation Fractional Brownian Motion Optimal Forecast
DOI10.1080/14697688.2023.2297730
URLView the original
Indexed BySCIE ; SSCI
Language英語English
WOS Research AreaBusiness & Economics ; Mathematics ; Mathematical Methods In Social Sciences
WOS SubjectBusiness, Finance ; Economics ; Mathematics, Interdisciplinary Applications ; Social Sciences, Mathematical Methods
WOS IDWOS:001142664000001
PublisherROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD2-4 PARK SQUARE, MILTON PARK, ABINGDON OX14 4RN, OXON, ENGLAND
Scopus ID2-s2.0-85184430105
Fulltext Access
Citation statistics
Document TypeJournal article
CollectionDEPARTMENT OF FINANCE AND BUSINESS ECONOMICS
Faculty of Business Administration
Corresponding AuthorZhang, Chen
Affiliation1.School of Economics, Fudan University, Shanghai, China
2.Shanghai Institute of International Finance and Economics, Shanghai, China
3.Department of Finance and Business Economics, Faculty of Business Administration, University of Macau, Taipa, Macao
Corresponding Author AffilicationFaculty of Business Administration
Recommended Citation
GB/T 7714
Wang, Xiaohu,Yu, Jun,Zhang, Chen. On the optimal forecast with the fractional Brownian motion[J]. Quantitative Finance, 2024, 24(2), 337-346.
APA Wang, Xiaohu., Yu, Jun., & Zhang, Chen (2024). On the optimal forecast with the fractional Brownian motion. Quantitative Finance, 24(2), 337-346.
MLA Wang, Xiaohu,et al."On the optimal forecast with the fractional Brownian motion".Quantitative Finance 24.2(2024):337-346.
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