Residential College | false |
Status | 已發表Published |
On the optimal forecast with the fractional Brownian motion | |
Wang, Xiaohu1,2; Yu, Jun3; Zhang, Chen3 | |
2024-01 | |
Source Publication | Quantitative Finance |
ABS Journal Level | 3 |
ISSN | 1469-7688 |
Volume | 24Issue: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. |
Keyword | Conditional Expectation Fractional Brownian Motion Optimal Forecast |
DOI | 10.1080/14697688.2023.2297730 |
URL | View the original |
Indexed By | SCIE ; SSCI |
Language | 英語English |
WOS Research Area | Business & Economics ; Mathematics ; Mathematical Methods In Social Sciences |
WOS Subject | Business, Finance ; Economics ; Mathematics, Interdisciplinary Applications ; Social Sciences, Mathematical Methods |
WOS ID | WOS:001142664000001 |
Publisher | ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD2-4 PARK SQUARE, MILTON PARK, ABINGDON OX14 4RN, OXON, ENGLAND |
Scopus ID | 2-s2.0-85184430105 |
Fulltext Access | |
Citation statistics | |
Document Type | Journal article |
Collection | DEPARTMENT OF FINANCE AND BUSINESS ECONOMICS Faculty of Business Administration |
Corresponding Author | Zhang, Chen |
Affiliation | 1.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 Affilication | Faculty 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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