Statistical estimation errors of VaR under ARCH returns |
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Authors: | Hiroyuki Taniai Masanobu Taniguchi |
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Affiliation: | 1. ISRO and ECARES, Université Libre de Bruxelles, 50 Avenue Roosevelt, CP114, B-1050 Bruxelles, Belgium;2. Department of Mathematical Sciences, School of Science and Engineering, Waseda University, Tokyo 169-8555, Japan |
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Abstract: | 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. |
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Keywords: | 62E20 62M10 91B30 |
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