The Improved Value-at-Risk for Heteroscedastic Processes and Their Coverage Probability. (10th March 2020)

• Record Type: Journal Article
• Authors: Syuhada, Khreshna
• Other Names: Psaradakis Zacharias Academic Editor.
• Is Part Of: Journal of probability and statistics. Volume 2020(2020)
• Publication Date: 2020-03-10
• Subjects: Probabilities -- Periodicals; Mathematical statistics -- Periodicals; Mathematical statistics; Probabilities; Periodicals; 519
• DOI: 10.1155/2020/7638517
• Languages: English
• ISSNs: 1687-952X

Abstract

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.