Statistical estimation errors of VaR under ARCH returns

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• 作者：Hiroyuki Taniai ; Masanobu Taniguchi
• 关键词：Value-at-risk ; ARCH model ; Residual empirical process ; Functional delta method ; Discretized estimator
• 刊名：Journal of Statistical Planning and Inference
• 出版年：2008
• 出版时间：1 November 2008
• 年：2008
• 卷：138
• 期：11
• 页码：3568-3577
• 全文大小：244 K

文摘

In this paper we discuss some problems of existing methods for calculating the Value-at-Risk (VaR) in ARCH setting. It should be noted that the commonly used approaches often confuse the true innovations with the empirical residuals, i.e., estimation errors for unknown ARCH parameters are ignored. We adjust this by using the asymptotics of the residual empirical process, and propose a feasible VaR which, according to the spirit of VaR, keeps the assets away from a specified risk with high confidence level. Its meaningfulness in comparison with the usual VaR will be illustrated clearly by numerical studies.