Prague Economic Papers 2008, 17(3):243-253 | DOI: 10.18267/j.pep.332

An empirical application of a two-factor model of stochastic volatility

Alexandr Kuchynka
University of West Bohemia in Pilsen, Faculty of Economics; Institute of Information Theory and Automation of the ASCR (alexk@kso.zcu.cz).

This contribution focuses on the modelling of volatility of returns in Czech and US stock markets using a two-factor stochastic volatility model, i.e. the volatility process is modeled as a superposition of two autoregressive processes. As the volatility is not observable, the logarithm of the daily range is employed as the proxy. The estimation of parameters and volatility extraction are performed using the Kalman filter. We have obtained a meaningful decomposition of the volatility process into one highly persistent factor and another quickly mean-reverting factor. Moreover, we have shown that although the overall level of the volatility of returns is roughly the same in both markets, the US market exhibits substantially lower volatility of the volatility process.

Keywords: volatility, stochastic volatility models, Kalman filter
JEL classification: C22, G15

Published: January 1, 2008  Show citation

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Kuchynka, A. (2008). An empirical application of a two-factor model of stochastic volatility. Prague Economic Papers, 17(3), 243-253. doi: 10.18267/j.pep.332
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    References

    1. Alizadeh, S., Brandt, M., Diebold, F. (2002), "Range-Based Estimation of Stochastic Volatility Models". Journal of Finance, 57, pp. 1047-1091. Go to original source...
    2. Andersen, T. G., Bollerslev, T., Diebold, F. X., Labys, P. (2001), "The Distribution of Realized Exchange Rate Volatility". Journal of the American Statistical Association, 96, pp. 42- 55. Go to original source...
    3. Barndorff-Nielsen, O. (2001), "Superposition of Ornstein-Uhlenbeck Type Processes". Theory Prob. Its Appl., 45, pp. 175-194. Go to original source...
    4. Barndorff-Nielsen, O. E., Shepard, N. (2001), "Non-Gaussian Ornstein-Uhlenbeck-Based Models and Some of their Uses in Financial Economic". Journal of the Royal Statistical Society. Series B 63, pp. 167-241. Go to original source...
    5. Bollerslev, T. (1986), "Generalized Autoregressive Conditional Heteroskedasticity". Journal of Econometrics, 31, pp. 307-327. Go to original source...
    6. Christensen, K., Podolskij, M. (2007), "Realized Range-Based Estimation of Integrated Variance". Journal of Econometrics, 141 (2), pp. 323-349. Go to original source...
    7. Ding, Z., Granger, C. W. J. (1996), "Modeling Volatility Persistence of Speculative Returns: A New Approach". Journal of Econometrics, 73 (1), pp. 185-215. Go to original source...
    8. Engle, R. F. (1982), "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation". Econometrica, 50, pp. 987-1007. Go to original source...
    9. Feller, W. (1951), "The Asymptotic Distribution of the Range of Sums of independent Random Variables". Annals of Mathematical Statistics, 22, pp. 427-432. Go to original source...
    10. Garman, M., Klass, M. J. (1980), "On the Estimation of Security Price Volatilities from Historical Data". Journal of Business, 53, pp. 67-78. Go to original source...
    11. Hamilton, J. (1994), Time Series Analysis. Princeton : Princeton University Press.
    12. Harvey, A. C., Ruiz, E., Shepard, N. (1994), "Multivariate Stochastic Variance Models". Review Economic Studies, 61, pp. 247-264. Go to original source...
    13. Hull, J., White, A. (1987), "The Pricing of Options on Assets with Stochastic Volatilities". Journal of Finance, 42, pp. 281-300. Go to original source...
    14. Lebaron, B. (2001), "Stochastic Volatility as a Simple Generator of Apparent Financial Power Laws and Long Memory". Quantitative Finance, 1 (6), pp. 621-31. Go to original source...
    15. Martens, M., Van Dijk, D. (2007), "Measuring Volatility with the Realized Range". Journal of Econometrics, 138, pp. 181-207. Go to original source...
    16. Parkinson, M. (1980), "The Extreme Value Method for Estimating the Variance of the Rate of Return". Journal of Business, 53 (1), pp. 61-65. Go to original source...
    17. Rogers, L. C. G., Satchell, S. E. (1991),"Estimating Variances from High, Low, and Closing Prices". Annals of Applied Probability, 1 (4), pp. 504-512. Go to original source...
    18. Ruiz, E. (1994), "Quasi-Maximum Likelihood Estimation of Stochastic Volatility Models". Journal of Econometrics, 63, pp. 289-306. Go to original source...
    19. Taylor, S. J. (1982), "Financial Returns Modelled by the Product of two Stochastic Processes a Study of Daily Sugar Prices 1961-79", in Anderson, O. D., ed., Time Series Analysis: Theory and Practice, 1. Amsterdam : North-Holland, pp. 203-226.

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