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The Improved Value-at-Risk for Heteroscedastic Processes and Their Coverage Probability

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  • Khreshna Syuhada

Abstract

A risk measure commonly used in financial risk management, namely, Value-at-Risk (VaR), is studied. In particular, we find a VaR forecast for heteroscedastic processes such that its (conditional) coverage probability is close to the nominal. To do so, we pay attention to the effect of estimator variability such as asymptotic bias and mean square error. Numerical analysis is carried out to illustrate this calculation for the Autoregressive Conditional Heteroscedastic (ARCH) model, an observable volatility type model. In comparison, we find VaR for the latent volatility model i.e., the Stochastic Volatility Autoregressive (SVAR) model. It is found that the effect of estimator variability is significant to obtain VaR forecast with better coverage. In addition, we may only be able to assess unconditional coverage probability for VaR forecast of the SVAR model. This is due to the fact that the volatility process of the model is unobservable.

Suggested Citation

  • Khreshna Syuhada, 2020. "The Improved Value-at-Risk for Heteroscedastic Processes and Their Coverage Probability," Journal of Probability and Statistics, Hindawi, vol. 2020, pages 1-5, March.
    • Handle: RePEc:hin:jnljps:7638517
    DOI: 10.1155/2020/7638517
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    Cited by:

    1. Syuhada, Khreshna & Hakim, Arief & Suprijanto, Djoko & Muchtadi-Alamsyah, Intan & Arbi, Lukman, 2022. "Is Tether a safe haven of safe haven amid COVID-19? An assessment against Bitcoin and oil using improved measures of risk," Resources Policy, Elsevier, vol. 79(C).
    2. Bony Josaphat & Khreshna Syuhada, 2020. "Dependent Conditional Value-at-Risk for Aggregate Risk Models," Papers 2009.02904, arXiv.org.

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