Advertisement

Automation and Remote Control

, Volume 79, Issue 9, pp 1687–1702 | Cite as

Nonparametric Estimation of Volatility and Its Parametric Analogs

  • A. V. Dobrovidov
  • V. E. Tevosian
Control Sciences
  • 3 Downloads

Abstract

This paper suggests a nonparametric method for stochastic volatility estimation and its comparison with other widespread econometric algorithms. A major advantage of this approach is that the volatility can be estimated even in the case of its completely unknown probability distribution. As demonstrated below, the new method has better characteristics against the popular parametric algorithms based on the GARCH model and Kalman filter.

Keywords

stochastic volatility nonparametric estimation of signals Kalman filter GARCH Taylor model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Merton, E., Theory of Rational Optiopricing, Bell J. Econom. Manage. Sci., 1973, vol. 4, pp. 141–183.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Busse, J., Volatility Timing in Mutual Funds: Evidence from Daily Returns, Rev. Financ. Stud., 1999, vol. 12, no. 5, pp. 1009–1041.CrossRefGoogle Scholar
  3. 3.
    Fleming, J., Kirby, C., and Ostdiek, B., The Economic Value of Volatility Timing, J. Finance, 2001, vol. 56, no. 1, pp. 329–352.CrossRefGoogle Scholar
  4. 4.
    Fleming, J., Kirby, C., and Ostdiek, B., The Economic Value of Volatility Timing Using “Realized” Volatility, J. Finance, 2003, vol. 67, no. 3, pp. 473–509.Google Scholar
  5. 5.
    Yao, Q. and Tong, H., Quantifying the Influence of Initial Values on Nonlinear Prediction, J. Royal Statist. Soc., 1994, ser. B56, pp. 701–725.zbMATHGoogle Scholar
  6. 6.
    Ziegelmann, F., Nonparametric Estimation of Volatility Functions: The Local Exponential Estimator, Econometr. Theory, 2002, vol. 18, pp. 985–91.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Duffie, D., Pan, J., and Singleton, K., Transform Analysis and Asset Pricing for Affine Jump-Diffusions, Econometrica, 2000, vol. 68, no. 6, pp. 1343–1376.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Jacquier, E., Polson, N., and Rossi, P., Bayesian Analysis of Stochastic Volatility Models, J. Business Econom. Statist., 1994, vol. 12, pp. 371–389.zbMATHGoogle Scholar
  9. 9.
    Bandi, F. and Reno, R., Nonparametric Stochastic Volatility, Working Paper, 2016. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1158438 (Accessed July 4, 2017).Google Scholar
  10. 10.
    Dobrovidov, A.V., Koshkin, G.M., and Vasiliev, V.A., Non-parametric Models and Statistical Inference from Dependent Observations, USA: Kendrick Press, 2012.zbMATHGoogle Scholar
  11. 11.
    Bollerslev, T., Generalized Autoregressive Conditional Heteroskedasticity, J. Econometr., 1986, vol. 31, pp. 307–327.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Taylor, S., Modelling Financial Times Series, New York: Wiley, 1986.zbMATHGoogle Scholar
  13. 13.
    Shiryaev, A.N., Osnovy stokhasticheskoi finansovoi matematiki (Fundamentals of Stochastic Financial Mathematics), Moscow: Fazis, 1998.Google Scholar
  14. 14.
    Shiryaev, A.N., Veroyatnost’ (Probability), Moscow: Nauka, 1989, 2nd. ed.zbMATHGoogle Scholar
  15. 15.
    Mills, T.C., The Econometric Modelling of Financial Time Series, Cambridge: Cambridge Univ. Press, 1999, 2nd ed.CrossRefzbMATHGoogle Scholar
  16. 16.
    Harvey, A.C., Forecasting Structural Time Series Models and the Kalman Filter, Cambridge: Cambridge Univ. Press, 1989.Google Scholar
  17. 17.
    Kalman, R., A New Approach to Linear Filtering and Prediction Problems, J. Basic Eng., 1960, vol. 82, pp. 34–45.Google Scholar
  18. 18.
    Theoret, E. and Eacicot, F., Forecasting Stochastic Volatility Using the Kalman Filter: An Application to Canadian Interest Rates and Price-Earnings Ratio, Munich Personal EePEc Archive, 2010. https://mpra.ub.uni-muenchen.de/35911/1/MPRA paper 35911.pdf (Accessed July 4, 2017).Google Scholar
  19. 19.
    Dobrovidov, A.V., Nonparametric Methods of Nonlinear Filtering of Stationary Random Sequences, Autom. Remote Control, 1983, no. 6, pp. 757–768.MathSciNetzbMATHGoogle Scholar
  20. 20.
    Kushner, H.J., On the Dynamical Equations of Conditional Probability Density Functions with Applications to Optimal Stochastic Control Theory, J. Math. Anal. Appl., 1964, vol. 8, no. 2, pp. 332–344.MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Stratonovich, R.L., Uslovnye markovskie protsessy i ikh primenenie k teorii optimal’nogo upravleniya (Conditional Markov Processes and Their Application in Optimal Control Theory), Moscow: Mosk. Gos. Univ., 1966.Google Scholar
  22. 22.
    Tikhonov, A.N., Ill-posed Problems of Linear Algebra and a Stable Method for Their Solution, Dokl. Akad. Nauk SSSR, 1965, vol. 163, no. 3, pp. 591–594.MathSciNetGoogle Scholar
  23. 23.
    Hall, P., Marron, J., and Park, B., Smoothed Cross-Validation, Probab. Theory Relat. Fields, 1992, vol. 90, pp. 1–20.MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Dobrovidov, A.V. and Rud’ko, I.M., Bandwidth Selection in Nonparametric Estimator of Density Derivative by Smoothed Cross-Validation Method, Autom. Remote Control, 2010, vol. 71, no. 2, pp. 209–224.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Trapeznikov Institute of Control SciencesRussian Academy of SciencesMoscowRussia

Personalised recommendations