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Efficient estimation of financial risk by regressing the quantiles of parametric distributions: An application to CARR models

Author

Listed:
  • Chan Jennifer So Kuen
  • Nitithumbundit Thanakorn
  • Peiris Shelton

    (The University of Sydney, School of Mathematics and Statistics, Rm 817 Carslaw Building,Sydney, New South Wales, 2006, Australia)

  • Ng Kok-Haur

    (Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur, 50603 Lembah Pantai, Malaysia)

Abstract

Risk measures such as value-at-risk (VaR) and expected shortfall (ES) may require the calculation of quantile functions from quantile regression models. In a parametric set-up, we propose to regress directly on the quantiles of a distribution and demonstrate a method through the conditional autoregressive range model which has increasing popularity in recent years. Two flexible distribution families: the generalised beta type two on positive support and the generalised-t on real support (which requires log transformation) are adopted for the range data. Then the models are extended to allow the volatility dynamic and compared in terms of goodness-of-fit. The models are implemented using the module fmincon in Matlab under the classical likelihood approach and applied to analyse the intra-day high-low price ranges from the All Ordinaries index for the Australian stock market. Quantiles and upper-tail conditional expectations evaluated via VaR and ES respectively are forecast using the proposed models.

Suggested Citation

  • Chan Jennifer So Kuen & Nitithumbundit Thanakorn & Peiris Shelton & Ng Kok-Haur, 2019. "Efficient estimation of financial risk by regressing the quantiles of parametric distributions: An application to CARR models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 23(2), pages 1-22, April.
    • Handle: RePEc:bpj:sndecm:v:23:y:2019:i:2:p:22:n:4
    DOI: 10.1515/snde-2017-0012
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    References listed on IDEAS

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