Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Expected shortfall estimation using kernel machines

  • Received : 2013.02.01
  • Accepted : 2013.04.01
  • Published : 2013.05.31
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Abstract

In this paper we study four kernel machines for estimating expected shortfall, which are constructed through combinations of support vector quantile regression (SVQR), restricted SVQR (RSVQR), least squares support vector machine (LS-SVM) and support vector expectile regression (SVER). These kernel machines have obvious advantages such that they achieve nonlinear model but they do not require the explicit form of nonlinear mapping function. Moreover they need no assumption about the underlying probability distribution of errors. Through numerical studies on two artificial an two real data sets we show their effectiveness on the estimation performance at various confidence levels.

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References

  1. Artzner, P., Delbaen, F., Eber, J. M. and Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9, 203-28. https://doi.org/10.1111/1467-9965.00068
  2. Bae, J., Hwang, C. and Shim, J. (2012). Two-step LS-SVR for censored regression. Journal of the Korean Data & Information Science Society, 23, 393-401. https://doi.org/10.7465/jkdi.2012.23.2.393
  3. Bollerslev, T. (1987). A conditional heteroskedastic time series model for speculative prices and rates of returns. Review of Economics and Statistics, 69, 542-547. https://doi.org/10.2307/1925546
  4. Cai, Z. and Wang, X. (2008). Nonparametric estimation of conditional VaR and expected shortfall. Journal of Econometrics, 147, 120-130. https://doi.org/10.1016/j.jeconom.2008.09.005
  5. Chen, S.X. (2008). Nonparametric estimation of expected shortfall. Journal of Financial Econometrics, 6, 87-107.
  6. Efron, B. (1991). Regression percentiles using asymmetric squared error loss. Statistica Sinica, 1, 93-125.
  7. He, X. (1997). Quantile curves without crossing. The American Statistician, 51, 86-192.
  8. Hwang, C. and Shim, J. (2011). Cox proportional hazard model with L1 penalty. Journal of the Korean Data & Information Science Society, 22, 613-618.
  9. Hwang, C. and Shim, J. (2012). Mixed effects least squares support vector machine for survival data analysis. Journal of the Korean Data & Information Science Society, 23, 739-748. https://doi.org/10.7465/jkdi.2012.23.4.739
  10. Jorion, P. (2007). Value at risk: The new benchmark for managing financial risk, McGraw-Hill, New York.
  11. Kato, K. (2012). Weighted Nadaraya-Watson estimation of conditional expected shortfall. Journal of Financial Econometrics, 10, 265-291. https://doi.org/10.1093/jjfinec/nbs002
  12. Kuhn, H. W. and Tucker, A. W. (1951). Nonlinear programming. In Proceedings of 2nd Berkeley Symposium, University of California Press, Berkeley, 481-492.
  13. Leorato, S., Peracchi, F. and Tanase, A. (2012). Asymptotically ecient estimation of the conditional expected shortfall. Computational Statistics and Data Analysis, 56, 768-784. https://doi.org/10.1016/j.csda.2011.02.020
  14. Li, Y., Liu, Y. and Ji, Z. (2007). Quantile regression in reproducing kernel Hilbert spaces. Journal of the American Statistical Association, 102, 255-268. https://doi.org/10.1198/016214506000000979
  15. Mercer, J. (1909). Functions of positive and negative type and their connection with theory of integral equations. Philosophical Transactions of Royal Society A, 415-446.
  16. Shim, J. and Lee, J. (2010). Restricted support vector quantile regression without crossing. Journal of the Korean Data & Information Science Society, 21, 1319-1325.
  17. Shim, J., Kim, Y., Lee, J. and Hwang, C. (2012). Estimating value at risk with semiparametric support vector quantile regression. Computational Statistics, 27, 685-700. https://doi.org/10.1007/s00180-011-0283-z
  18. Shim, J. and Seok, K. (2012). Semiparametric kernel logistic regression with longitudinal data. Journal of the Korean Data & Information Science Society, 23, 385-392. https://doi.org/10.7465/jkdi.2012.23.2.385
  19. Suykens, J. A. K. and Vanderwalle, J. (1999). Least square support vector machine classifier. Neural Processing Letters, 9, 293-300. https://doi.org/10.1023/A:1018628609742
  20. Takeuchi, I., Le, Q. V., Sears, T. D. and Smola, A. J. (2006). Nonparametric quantile estimation. Journal of Machine Learning Research, 7, 1231-1264.
  21. Taylor, J. W. (2000). A quantile regression neural network approach to estimating the conditional density of multiperiod returns. Journal of Forecasting, 19, 299-311. https://doi.org/10.1002/1099-131X(200007)19:4<299::AID-FOR775>3.0.CO;2-V
  22. Taylor, J. W. (2008a). Estimating value at risk and expected shortfall using expectiles. Journal of Financial Econometrics, 6, 231-252.
  23. Taylor, J. W. (2008b). Using exponentially weighted quantile regression to estimate value at risk and expected shortfall. Journal of Financial Econometrics, 6, 382-406. https://doi.org/10.1093/jjfinec/nbn007
  24. Vapnik, V. N. (1995). The nature of statistical learning theory, Springer, New York.
  25. Wang, Y., Wang, S. and Lai, K. (2011). Measuring financial risk with generalized asymmetric least squares regression. Applied Soft Computing, 11, 5793-5800. https://doi.org/10.1016/j.asoc.2011.02.018
  26. Yuan, M. (2006). GACV for quantile smoothing splines. Computational Statistics & Data Analysis, 50, 813-829. https://doi.org/10.1016/j.csda.2004.10.008
  27. Zhu, D. and Galbraith, J. W. (2011). Modeling and forecasting expected shortfall with the generalized asymmetric Student-t and asymmetric exponential power distributions. Journal of Empirical Finance, 18, 765-778. https://doi.org/10.1016/j.jempfin.2011.05.006

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