STOCK MARKET FLUCTUATIONS SIMULATION WITHIN LOWLY VOLATILE AND HIGHLY VOLATILE PERIODS
Abstract
The simulation of stock price fluctuations is analyzed. The statistical criteria application allows drawing the conclusion on the investigated models’ validity. Alongside with well-known Kolmogorov-Smirnov and Anderson-Darling criteria, comparatively new Christoffersen and Berkowitz criteria are used to assess interval predictions. Berkowitz criterion is particularly effective when used to assess extreme price leaps within highly volatile periods, since it gives good results also for a small number of observations. It is shown that the customarily used time-series models with normal distribution and with Student distribution are applicable exclusively during relatively stable periods. Under the unstable conditions at the financial markets, models by means of which it is possible to describe a high probability of great price leaps are required. The time-series model with the heavy tailed distribution is studied. The recommendations on the portfolio management under the crisis time are provided on the basis of the performed calculations.
Keywords
ARMA-GARCH model,
Value-at-Risk (VaR),
Average Value-at-Risk (AVaR),
time series,
heavy-tailed distributions.
Supporting agencies: The research is done with the support of the Russian Presidential Scholarship (2011—2012).
References
1. Engle, R. Autoregressive conditional heteroscedasticity with estimates of VaRiance of united kingdom inflation. Econometrica, 1982, vol. 50, pp. 987–1008.
2. Bollerslev, T. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 1986, vol. 31, no. 3, pp. 307–327.
3. Engle, R. F., Patton, A. What good is a volatility model? Quantitative Finance, 2001, vol. 50, pp. 237–245.
4. Belousov, S. M. Modelirovaniye volatilnosti so skachkami: primeneniye k rossiyskomu i ameri-kanskomu fondovym rynkam. [Simulation of volatility with discrete steps: applying to the Russian and American stock markets.] Kvantil, 2006, no. 1, pp. 101–110 (in Russian).
5. Kim, Y. S., et al. Tempered stable and tempered infinitely divisible GARCH models. Journal of Banking and Finance, 2010, no. 34, pp. 2096–2109.
6. Kim, Y. S., et al. The modified tempered stable distribution, GARCH-models and option pricing. Probability and Mathematical Statistics, 2009, vol. 29, no. 1, pp. 91–117.
7. Kim, Y. S., et al. Time series analysis for financial market meltdowns. Journal of Banking and Finance, 2011, no. 35, pp. 1879–1891.
8. Bianchi, M. L., et al. Tempered infinitely divisible distributions and processes. Theory of Probabi-lity and Its Applications, Society for Industrial and Applied Mathematics, 2010, vol. 55, no. 1, pp. 58–86.
9. Buldashev, S. V. Statistika dlya treyderov. [Statistics for traders.] Moscow : Kompaniya Sputnik, 2003, 244 p. (in Russian).
10. Christoffersen, P. F. Evaluating interval forecasts. International Economic Review, 1998, vol. 39, no. 4, pp. 841–862.
Review
For citations:
Kirillov K.V. STOCK MARKET FLUCTUATIONS SIMULATION WITHIN LOWLY VOLATILE AND HIGHLY VOLATILE PERIODS. Vestnik of Don State Technical University. 2013;13(7-8):5-14. (In Russ.) https://doi.org/10.12737/2014
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