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The data-based choice of bandwidth for kernel quantile estimator of VaR. (English) Zbl 1255.91189

Summary: Value-at-Risk is an important risk measure, has been wildly applied in market practice and financial risk measurement. We use the smooth kernel estimator for the quantile proposed by E. Parzen [J. Am. Stat. Assoc. 74, 105–122 (1979; Zbl 0407.62001)] as a VaR estimator and propose a data-based choice method of optimal bandwidth via normal reference distribution, which is easy to compute. The simulations show that the choice method of bandwidth is effective, and the smooth kernel estimator has better performance than the sample quantile estimator.

MSC:

91B30 Risk theory, insurance (MSC2010)
91B82 Statistical methods; economic indices and measures
62-07 Data analysis (statistics) (MSC2010)
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G10 Nonparametric hypothesis testing
62G05 Nonparametric estimation

Citations:

Zbl 0407.62001
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