Journal of Risk
ISSN:
1465-1211 (print)
1755-2842 (online)
Editor-in-chief: Farid AitSahlia
Need to know
- Exact Value-at-Risk (VaR) and Expected Shortfall (ES) risk measures cannot be found because of parameter estimation errors.
- Consequently, approximate VaR and ES risk measures are used.
- The difference between approximate and exact risk measures is found to be substantial.
Abstract
For a given time series of daily losses that display volatility clustering, the exact next- day and ten-day value-at-risk (VaR) and expected shortfall (ES) are unknown. The usual procedure is to approximate these values by replacing true parameter values with estimates in the formulas for VaR and ES. Parameter estimation errors for a GARCH(1,1) model for this time series lead to approximate VaR and ES that differ from the exact VaR and ES, respectively. Accurate estimation of the VaR and ES is very important for the proper management of financial risks. In this paper, we find linear regression models in which the response variable is the approximate VaR (ES) and the explanatory variable is the exact VaR (ES). We use these linear regression models to determine the properties of the approximate VaR (ES), conditional on the corresponding exact value. For a given value of the exact VaR (ES), the approximate VaR (ES) is close to being an unbiased estimator of the corresponding exact value, but it may differ from this exact value by more than 10% of the exact value with substantial probability.
Copyright Infopro Digital Limited. All rights reserved.
As outlined in our terms and conditions, https://www.infopro-digital.com/terms-and-conditions/subscriptions/ (point 2.4), printing is limited to a single copy.
If you would like to purchase additional rights please email info@risk.net
Copyright Infopro Digital Limited. All rights reserved.
You may share this content using our article tools. As outlined in our terms and conditions, https://www.infopro-digital.com/terms-and-conditions/subscriptions/ (clause 2.4), an Authorised User may only make one copy of the materials for their own personal use. You must also comply with the restrictions in clause 2.5.
If you would like to purchase additional rights please email info@risk.net