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.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Merton, E., Theory of Rational Optiopricing, Bell J. Econom. Manage. Sci., 1973, vol. 4, pp. 141–183.
Busse, J., Volatility Timing in Mutual Funds: Evidence from Daily Returns, Rev. Financ. Stud., 1999, vol. 12, no. 5, pp. 1009–1041.
Fleming, J., Kirby, C., and Ostdiek, B., The Economic Value of Volatility Timing, J. Finance, 2001, vol. 56, no. 1, pp. 329–352.
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.
Yao, Q. and Tong, H., Quantifying the Influence of Initial Values on Nonlinear Prediction, J. Royal Statist. Soc., 1994, ser. B56, pp. 701–725.
Ziegelmann, F., Nonparametric Estimation of Volatility Functions: The Local Exponential Estimator, Econometr. Theory, 2002, vol. 18, pp. 985–91.
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.
Jacquier, E., Polson, N., and Rossi, P., Bayesian Analysis of Stochastic Volatility Models, J. Business Econom. Statist., 1994, vol. 12, pp. 371–389.
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).
Dobrovidov, A.V., Koshkin, G.M., and Vasiliev, V.A., Non-parametric Models and Statistical Inference from Dependent Observations, USA: Kendrick Press, 2012.
Bollerslev, T., Generalized Autoregressive Conditional Heteroskedasticity, J. Econometr., 1986, vol. 31, pp. 307–327.
Taylor, S., Modelling Financial Times Series, New York: Wiley, 1986.
Shiryaev, A.N., Osnovy stokhasticheskoi finansovoi matematiki (Fundamentals of Stochastic Financial Mathematics), Moscow: Fazis, 1998.
Shiryaev, A.N., Veroyatnost’ (Probability), Moscow: Nauka, 1989, 2nd. ed.
Mills, T.C., The Econometric Modelling of Financial Time Series, Cambridge: Cambridge Univ. Press, 1999, 2nd ed.
Harvey, A.C., Forecasting Structural Time Series Models and the Kalman Filter, Cambridge: Cambridge Univ. Press, 1989.
Kalman, R., A New Approach to Linear Filtering and Prediction Problems, J. Basic Eng., 1960, vol. 82, pp. 34–45.
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).
Dobrovidov, A.V., Nonparametric Methods of Nonlinear Filtering of Stationary Random Sequences, Autom. Remote Control, 1983, no. 6, pp. 757–768.
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.
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.
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.
Hall, P., Marron, J., and Park, B., Smoothed Cross-Validation, Probab. Theory Relat. Fields, 1992, vol. 90, pp. 1–20.
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.V. Dobrovidov, V.E. Tevosian, 2017, published in Problemy Upravleniya, 2017, No. 4, pp. 26–36.
Rights and permissions
About this article
Cite this article
Dobrovidov, A.V., Tevosian, V.E. Nonparametric Estimation of Volatility and Its Parametric Analogs. Autom Remote Control 79, 1687–1702 (2018). https://doi.org/10.1134/S0005117918090126
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117918090126