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Modelling and forecasting stock volatility and return: a new approach based on quantile Rogers–Satchell volatility measure with asymmetric bilinear CARR model

  • Shay Kee Tan , Jennifer So Kuen Chan and Kok Haur Ng ORCID logo EMAIL logo


This paper proposes quantile Rogers–Satchell (QRS) measure to ensure robustness to intraday extreme prices. We add an efficient term to correct the downward bias of Rogers–Satchell (RS) measure and provide scaling factors for different interquantile range levels to ensure unbiasedness of QRS. Simulation studies confirm the efficiency of QRS measure relative to the intraday squared returns and RS measures in the presence of extreme prices. To smooth out noises, QRS measures are fitted to the CARR model with different asymmetric mean functions and error distributions. By comparing to two realised volatility measures as proxies for the unobserved true volatility, results from Standard and Poor 500 and Dow Jones Industrial Average indices show that QRS estimates using asymmetric bilinear mean function provide the best in-sample model fit based on two robust loss functions with heavier penalty for under-prediction. These fitted volatilities are then incorporated into return models to capture the heteroskedasticity of returns. Model with a constant mean, Student-t errors and QRS estimates gives the best in-sample fit. Different value-at-risk (VaR) and conditional VaR forecasts are provided based on this best return model. Performance measures including Kupiec test for VaRs are evaluated to confirm the accuracy of the VaR forecasts.

Corresponding author: Kok Haur Ng, Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Lembah Pantai, Kuala Lumpur, Malaysia; and School of Mathematics and Statistics, The University of Sydney, Sydney 2006, NSW, Australia, E-mail:

Funding source: Fundamental Research Grant Scheme (FRGS) of Ministry of Higher Education (MOHE), Malaysia

Award Identifier / Grant number: FP041-2017A (Ref. code: FRGS/1/2017/STG06/UM/02/9)

Funding source: Postgraduate Research Grant (PPP) of the University of Malaya

Award Identifier / Grant number: PG037-2016A

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: Fundamental Research Grant Scheme (FRGS) with grant no: FP041-2017A (Ref. code: FRGS/1/2017/STG06/UM/2019) of Ministry of Higher Education (MoHE), Malaysia; Postgraduate Research Grant with grant no: PG037-2016A of the University of Malaya.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.


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Supplementary Material

The online version of this article offers supplementary material (

Received: 2019-09-03
Revised: 2021-05-17
Accepted: 2021-05-18
Published Online: 2021-06-08

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