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.
Highlights
Risk management and risk measures have become important topics to discuss among financial and actuarial practitioners as well as academia. ey have spent their efforts to seek better risk models and to apply these for real problems
VaR forecast is an application of the concept of the prediction limit for future observations, given a collection of random variables for losses
We demonstrate the calculation of the VaR forecast using the simulation algorithm of Kabaila [7] for computing some particular types of conditional expectations
Summary
Statistics Research Division, Institut Teknologi Bandung, Jalan Ganesa 10, Bandung 40132, Indonesia. We find a VaR forecast for heteroscedastic processes such that its (conditional) coverage probability is close to the nominal. 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. 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. We may only be able to assess unconditional coverage probability for VaR forecast of the SVAR model. Is is due to the fact that the volatility process of the model is unobservable We may only be able to assess unconditional coverage probability for VaR forecast of the SVAR model. is is due to the fact that the volatility process of the model is unobservable
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