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A Novel Multivariate Volatility Modeling for Risk Management in Stock Markets

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Abstract

Volatility modeling is crucial for risk management and asset allocation; this is an influential area in financial econometrics. The central requirement of volatility modeling is to be able to forecast volatility accurately. The literature review of volatility modeling shows that the approaches of model averaging estimation are commonly used to reduce model uncertainty in order to achieve a satisfactory forecasting reliability. However, those approaches attempt to forecast more reliable volatilities by integrating all forecasting outcomes equally from several volatility models. Forecasting patterns generated by each model may be similar. This may cause redundant computation without improving forecasting reliability. The proposed multivariate volatility modeling method which is called the fuzzy-method-involving multivariate volatility model (abbreviated as FMVM) classifies the individual models into smaller scale clusters and selects the most representative model in each cluster. Hence, repetitive but unnecessary computational burden can be reduced, and forecasting patterns from representative models can be integrated. The proposed FMVM is benchmarked against existing multivariate volatility models on forecasting volatilities of Hong Kong Hang Seng Index constituent stocks. Numerical results show that it can obtain relatively lower forecasting errors with less model complexity.

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References

  1. Christoffersen, P.F., Diebold, F.X.: How relevant is volatility forecasting for financial risk management? Rev. Econ. Stat.82, 12–23 (2000)

    Article  Google Scholar 

  2. Yiu, K.F.C.: Optimal portfolios under a value-at-risk constraint. J. Econ. Dyn. Control28(7), 1317–1334 (2004)

    Article MathSciNet MATH  Google Scholar 

  3. Jorion, P.: Value at Risk: The New Benchmark for Managing Financial Risk, 3rd edn. McGraw Hill Professional, New York (2006)

    Google Scholar 

  4. Yiu, K.F.C., Liu, J.Z., Siu, T.K., Ching, W.K.: Optimal portfolios with regime switching and value-at-risk constraint. Automatica46(6), 979–989 (2010)

    Article MathSciNet MATH  Google Scholar 

  5. Liu, J.Z., Yiu, K.F.C., Siu, T.K., Ching, W.K.: Optimal investment–reinsurance with dynamic risk constraint and regime switching. Scand. Actuar. J.2013(4), 263–285 (2013)

    Article MathSciNet MATH  Google Scholar 

  6. van den Broek, K.: Long-term insurance products and volatility under the Solvency II framework. Eur. Actuar. J.4(2), 315–334 (2014)

    Article MathSciNet MATH  Google Scholar 

  7. Yiu, K.F.C., Wang, S.Y., Mak, K.L.: Optimal portfolios under a value-at-risk constraint with applications to inventory control in supply chains. J. Ind. Manag. Optim.4(1), 81 (2008)

    Article MathSciNet MATH  Google Scholar 

  8. Wang, S.Y., Yiu, K.F.C., Mak, K.L.: Optimal inventory policy with fixed and proportional transaction costs under a risk constraint. Math. Comput. Model.58(9), 1595–1614 (2013)

    Article MathSciNet  Google Scholar 

  9. Bollerslev, T.: Generalized autoregressive conditional heteroskedasticity. J. Econom.31(3), 307–327 (1986)

    Article MathSciNet MATH  Google Scholar 

  10. Engle, R., Kroner, K.F.: Multivariate simultaneous generalized ARCH. Econom. Theory11(01), 122–150 (1995)

    Article MathSciNet  Google Scholar 

  11. Bollerslev, T.: Modelling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH model. Rev. Econ. Stat.72(3), 498–505 (1990)

  12. Alexander, C.O. (ed.): Orthogonal GARCH. In: Mastering Risk, vol. 2, pp. 21–38. Financial Times-Prentice Hall, London (2001)

  13. Engle, R.: Dynamic conditional correlation: a simple class of multivariate generalized autoregressive conditional heteroskedasticity models. J. Bus. Econ. Stat.20(3), 339–350 (2002)

    Article MathSciNet  Google Scholar 

  14. Cappiello, L., Engle, R.F., Sheppard, K.: Asymmetric dynamics in the correlations of global equity and bond returns. J. Financ. Econom.4(4), 537–572 (2006)

    Article  Google Scholar 

  15. Pesaran, M.H., Schleicher, C., Zaffaroni, P.: Model averaging in risk management with an application to futures markets. J. Empir. Finance16(2), 280–305 (2009)

    Article  Google Scholar 

  16. Batuwita, R., Palade, V.: FSVM-CIL: fuzzy support vector machines for class imbalance learning. IEEE Trans. Fuzzy Syst.18(3), 558–571 (2010)

    Article  Google Scholar 

  17. Batuwita, R., Palade, V., Bandara, D.C.: FSVM-CIL: fuzzy support vector machines for class imbalance learning. Int. J. Artif. Intell. Tools20(3), 425–455 (2011)

    Article  Google Scholar 

  18. Serguieva, A., Hunter, J.: Fuzzy interval methods in investment risk appraisal. Fuzzy Sets Syst.142(3), 443–466 (2004)

    Article MathSciNet MATH  Google Scholar 

  19. Chen, S.M., Chang, Y.C.: Multi-variable fuzzy forecasting based on fuzzy clustering and fuzzy rule interpolation techniques. Inf. Sci.180, 4772–4783 (2010)

    Article MathSciNet  Google Scholar 

  20. Bezdek, J.C., Ehrlich, R., Full, W.: FCM: the fuzzy c-means clustering algorithm. Comput. Geosci.10(2–3), 191–203 (1984)

    Article  Google Scholar 

  21. Pathak, A., Pal, N.R.: Clustering of mixed data by integrating fuzzy, probabilistic, and collaborative clustering framework. Int. J. Fuzzy Syst.18(3), 339–348 (2016)

  22. Zhang, T., Chen, L., Chen, C.P.: Clustering algorithm based on spatial shadowed fuzzy c-means and I-Ching operators. Int. J. Fuzzy Syst.18(4), 609–617 (2016)

    Article MathSciNet  Google Scholar 

  23. Dalman, H.: An interactive fuzzy goal programming algorithm to solve decentralized bi-level multiobjective fractional programming problem. arXiv preprintarXiv:1606.00927 (2016)

  24. Dalman, H., Güzel, N., Sivri, M.: A fuzzy set-based approach to multi-objective multi-item solid transportation problem under uncertainty. Int. J. Fuzzy Syst.18(4), 716–729 (2015)

  25. Dalman, H.: Uncertain programming model for multi-item solid transportation problem. Int. J. Mach. Learn. Cybern. 1–9 (2016)

  26. Andersen, T.G., Bollerslev, T., Diebold, F.X., Ebends, H.: Fuzzy interval methods in investment risk appraisal. J. Financ. Econ.61, 43–76 (2001)

    Article  Google Scholar 

  27. Sheppard, K.: MFE matlab function reference. Financ. Econom. (Computer software manual) (2009)

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Acknowledgement

This work was supported by the PolyU grant G-YBCV.

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, People’s Republic of China

    Zi-Kai Wei, Ka-Fai Cedric Yiu & Heung Wong

  2. Department of Electrical and Computer Engineering, Curtin University, Perth, Australia

    Kit-Yan Chan

Authors
  1. Zi-Kai Wei

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  2. Ka-Fai Cedric Yiu

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  3. Heung Wong

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  4. Kit-Yan Chan

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Corresponding author

Correspondence toKa-Fai Cedric Yiu.

Appendix: A Model Classification Example of Low-Dimensional Cases

Appendix: A Model Classification Example of Low-Dimensional Cases

Assume that we have 4 assets and use one-day-ahead forecasting. The classification results are shown in Tables4,5,6,7,8,9,10,11 and12. The first row in each table shows our benchmark. Other rows show different clustering results with the first model in each row/cluster being the representative model for this cluster; for instance, in Table12,DCC(2, 2) andADCC(2, 2) are grouped in cluster 6, and theDCC(2, 2) is the representative model.

Table 4 The 2-classes case
Table 5 The 3-classes case
Table 6 The 4-classes case
Table 7 The 5-classes case
Table 8 The 6-classes case
Table 9 The 7-classes case
Table 10 The 8-classes case
Table 11 The 9-classes case
Table 12 The 10-classes case

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Wei, ZK., Yiu, KF.C., Wong, H.et al. A Novel Multivariate Volatility Modeling for Risk Management in Stock Markets.Int. J. Fuzzy Syst.20, 116–127 (2018). https://doi.org/10.1007/s40815-017-0298-x

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