Forecasting Value-at-Risk Using High-Frequency Information
Abstract
:1. Introduction
2. Data
3. Forecasting Quantiles Using High-Frequency Information
3.1. Daily Close Quantile Forecasts
3.2. CI Quantile Forecasts
3.3. CF Quantile Forecasts
- CF Step 1: Compute quantile forecasts from regressing on each individual sub-sample,
- CF Step 2: Combine the quantile forecasts from Step 1 by some weighting methods for forecast combination. A simplest example of the combination methodology is the simple average:
3.4. Subsample-Averaging Quantile Forecasts
- SA Step 1:
- SA Step 2: Taking simple average, we get the quantile forecast
3.5. Bagging Daily Close Quantile Forecasts
- Bagging Step 1: Construct a bootstrap sample according to the empirical distribution of daily close returns. Run the quantile regression in Equation (4) by regressing on , obtain and compute the bootstrap Daily Close quantile forecast
- Bagging Step 2: Combine the quantile forecasts from Step 1 by some weighting methods for forecast combination. A simplest example of the combination is the simple average:
4. Out-of-Sample Quantile Forecasting Results
Daily-Close (mean tick lossx100) | 4.5816 | 15.1202 | 24.7583 | 48.3697 | 54.5713 | 48.6378 | 26.7932 | 16.5165 | 5.0059 |
Bagging Daily-Close | 0.9139 | 0.9826 | 0.9976 | 0.9935 | 0.9971 | 0.9980 | 0.9934 | 0.9938 | 0.9131 |
SA-Mean | 0.8803 | 0.9723 | 0.9877 | 0.9873 | 0.9990 | 0.9967 | 0.9882 | 0.9764 | 0.9513 |
SA-Median | 0.8903 | 0.9731 | 0.9916 | 0.9885 | 0.9994 | 0.9954 | 0.9905 | 0.9818 | 0.9699 |
CF-Mean | 0.9226 | 0.9718 | 0.9928 | 0.9938 | 0.9992 | 0.9943 | 0.9912 | 0.9750 | 0.9403 |
CF-Median | 0.9339 | 0.9746 | 0.9952 | 0.9939 | 0.9997 | 0.9952 | 0.9940 | 0.9805 | 0.9445 |
CF-PC (AIC) | 1.1006 | 1.0221 | 1.0273 | 1.0025 | 1.0097 | 1.0047 | 1.0224 | 0.9772 | 2.2536 |
CF-PC (BIC) | 1.0746 | 1.0103 | 0.9982 | 0.9948 | 0.9985 | 0.9944 | 1.0064 | 0.9938 | 2.0761 |
CF-PC () | 0.9253 | 0.9726 | 0.9892 | 0.9962 | 0.9985 | 0.9982 | 0.9993 | 0.9832 | 0.9562 |
CF-PC () | 0.9356 | 0.9792 | 0.9894 | 0.9973 | 0.9985 | 0.9983 | 0.9916 | 1.0034 | 0.9896 |
CF-PC () | 0.9853 | 0.9823 | 1.0012 | 0.9983 | 0.9992 | 1.0008 | 0.9884 | 0.9985 | 0.9607 |
CI-Unrestricted | 5.8885 | 2.0387 | 1.5619 | 1.1643 | 1.1971 | 1.2420 | 1.4362 | 1.8454 | 4.8916 |
CI-PC (AIC) | 1.0956 | 1.0340 | 1.0337 | 0.9914 | 1.0006 | 0.9980 | 0.9888 | 1.0278 | 0.9905 |
CI-PC (BIC) | 1.0456 | 1.0291 | 1.0284 | 0.9951 | 1.0004 | 0.9871 | 0.9891 | 0.9945 | 0.9967 |
CI-PC () | 0.9471 | 0.9675 | 1.0121 | 0.9983 | 1.0004 | 1.0018 | 1.0030 | 0.9952 | 0.9167 |
CI-PC () | 0.9589 | 0.9817 | 1.0132 | 0.9977 | 1.0033 | 1.0040 | 1.0095 | 0.9966 | 0.8947 |
CI-PC () | 0.9974 | 0.9752 | 1.0014 | 0.9984 | 1.0025 | 0.9955 | 1.0018 | 0.9879 | 1.0224 |
5. Conclusions
Acknowledgements
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- 1We are grateful to George Jiang who generously shared this high-frequency intra-day data with us. The data are extracted from the contemporaneous index levels recorded with the quotes of SPX options from the CBOE.
- 2To better comprehend this factor representation, if we think of the stock market as a vast pool of information and that price is determined by aggregate behavior of market participants, there may exist a few fundamental shocks to the market in a given day that ultimately determine the daily return at close. This small set of shocks (main forces) may be captured by the latent factors in the factor model Equation (9), or technically, by a few principal components of the big explanatory variable set , which contains as large as 156 variables capturing levels and volatilities of the market throughout the trading day.
- 3We thank a referee for this point.
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Huang, H.; Lee, T.-H. Forecasting Value-at-Risk Using High-Frequency Information. Econometrics 2013, 1, 127-140. https://doi.org/10.3390/econometrics1010127
Huang H, Lee T-H. Forecasting Value-at-Risk Using High-Frequency Information. Econometrics. 2013; 1(1):127-140. https://doi.org/10.3390/econometrics1010127
Chicago/Turabian StyleHuang, Huiyu, and Tae-Hwy Lee. 2013. "Forecasting Value-at-Risk Using High-Frequency Information" Econometrics 1, no. 1: 127-140. https://doi.org/10.3390/econometrics1010127