Modelagem e previsão de volatilidade determinística e estocástica para a série do Ibovespa
DOI:
https://doi.org/10.1590/1980-53572931imAbstract
The variance of an asset is the most important information for an investor that deals in
the financial markets. The measurement of that volatility can be done in two different
ways. The first one, deterministic case, is done by taking as a starting point the
knowledge of conditional variance. In the other approach, called stochastic volatility,
one does not know a priori the volatility of the asset. These models are used in many
different formulations to explain the specific characteristics observed in the financial
time series, such as volatility clustering, leverage effect and persistence of the volatility.
In this paper, the volatility of the Sdo Paulo Stock Exchange Index (Ibovespa) is modelled
by the two processes described above. The period analysed goes from july/94 until
october/98, include three critical periods of the world financial markets: the Mexican
crisis, the Asian crisis and finally the Russian debacle. The main conclusion is that both process perform quite well.
Downloads
References
AKGIRAY, V Conditional heteroscedasticity in time series of stock returns: evidence and forecasts. Journal ofBusiness, v. 62, n.l, 55-80, 1989.
BARCINSKI, A., ALMEIDA, B. C. P., GARCIA, M. G. P. & SILVEIRA, M. A. C. Estimação da volatilidade do retorno das ações brasileiras: um método alternativo à família GARCH. ResenhaBM&F, n. 116, p. 21-39, 1997.
BOLLERSLEV; T. Generalized autoregressive conditional heteroskedasticity.
Journal of Econometrics, 31, p. 307-27, 1986.
BOLLERSLEV; T. A conditionally heteroskedastic time series model for speculative prices and rates of return. The Review ofEconomics and Statistics, v. LXIX, n. 3, p. 542-47, 1987.
BRAUN, P. A., NELSON, D. B. E SUNIER, A. M. Good news, bad news, volatility, and betas. TheJournal ofFinance, v. 50, n. 5, 1995.
BUSTAMANTE, M. & FERNANDES, M. Um procedimento para análise da persistência na volatilidade. Anais do XVII Encontro Brasileiro de Econometria, Revista de Econometria, p. 203-223, 1995.
CHRISS, N. A. Black & Scholes and beyond - option pricing models. McGrall-Hill, 1997.
CORBJiA, M. M. R. L. & PEREIRA, P. L. V Modelos nao lineares em finanças: previsibilidade em mercados financeiros e aplicações a gestão de risco. Anais do XXEncontro Brasileiro de Econometria, v. 1, 1998, p. 427-448.
DAY, T. E. & LEWIS, C. M. Stock market volatility and the information content of stock index options. Journal ofEconometrics, 52, p. 267-87, 1992.
DING, Z., GRANGER, C. W J. & ENGLE, R. E A long memory property of stock market returns and a new model. Journal ofEmpirical Finance, p. 83-106, 1993.
DUARTE J., A. M. Simulacjao Monte Carlo para analise de op^oes. Resenha
BMtkF, n.115, p. 52-64,1997.
DUARTE J., A. M., PINHEIRO M. A., HEIL, T. B. B. Estimação da volatilidade de ativos e indices brasileiros. ResenhaBM&cF, n. Ill, p. 16-28, 1996.
ENGLE, R. E Autoregressive conditional heteroskedasticity with estimates of the variances of U.K. inflation. Econometrica, v. 50, n. 4, p. 987-1008, 1982.
ENGLE, R. E & BOLLERSLEy T. Modelling the persistence of conditional variances, {with (Escassion). Econometrics Reviews, 5, p. 1-50, 81-87,1986.
ENGLE, R. E, LILIEN, D. M. & ROBINS, R. P. Estimating time-varying risk premia in the term structure: the ARCH-M model. Econometrica, 55, p. 391-408, 1987.
ENGLE, R. E & NG, V K. Measuring and testing the impact of news on vohtihty. Journal of Finance, 4815, p. 1749-78, 1993.
FORNARI, E &MELE, A. Modeling the changing asymetry of conditional variances. Economics Letters, 50, p. 197-203, 1996.
GALVAO, A. B. C., PORTUGAL, M. S. & RIBEIRO, E. P. Volatilidade e causalidade; os efeitos da crise do Mexico sobre os mercados a vista e future de cambio e mdice de agoes no Brasil. Anais do no XIX Encontro Brasileiro de Econometria, v. 11, 1997, p. 755-774.
GIBBONS, M. R. & HESS, P Day of the week effects and asset returns. Journal ofBusiness, v. 4, n. 4, p. 579-596, 1981.
GLOSTEN, L. R., JAGANNATHAN, R. & RUNKLE, D. E. On the relation between expected value and the volatility ofthe nominal excess return on stocks. Journal ofFinance, 48, p. 1779-1801, 1993.
HAGERUD, G. E. A smooth transition ARCH model for asset returns. Working Paper Stockholm School ofEconomics, 1996.
HAGERUD, G. E. Modeling nordic stock returns with asymmetric GARCH models. Working Paper Series in Economics and Finance, n. 164, 1997.
HAMILTON, J. D. State space models. Handbook ofeconometrics, v. TV, cap. 50, p. 3039-3080, 1994.
HAMILTON, J. D. and SUSMEL, R. Autoregressive conditional heteroskedasticity and changes in rtgimc. Journal ofEconometrics, v. 64, p. 307-333, 1994.
HARVEY, A. C. Forecasting, structural time series models and Kalman filter. Cambridge University Press, 1996.
HERENCIA, M. E. Z. Volatilidade nos modelos ARCH e variancia estocastica: um estudo comparativo. Dissertafdo de Mestrado apresentada ao IMEUnicamp, 1997.
HERENCIA, M. E. Z. HOTTA, L. K. & PEREIRA, P. L. V Filtragem e previsao com modelos
de volatilidade: volatilidade estocastica versus GARCH. Revista Brasileira de Economia., v. 52, n. 2, p. 241-278, 1998.
JAMES, B. R. Probabilidade: um curso em mvel intermedidrio. Projeto Euclides, 2° ed., IMPA, 1996.
KIM, D., KON, S. J. Alternative models for the conditional heteroscedasticity of stock ctmtns. Journal ofBusiness, v. 67,n. 4, p. 563-598, 1994.
KRONER, K. Creating and using volatility forecasts. DerivativesQuartely, p. 39-53, 1996.
LAMOUREUX, C. G. & LASTRAPES, W D. Heteroskedasticity in stock return data; volume versus GARCH effects. Journal of Finance 45, p. 221-229, 1990.
NELSON, D. B. Conditional heteroskedasticity in asset returns; a new approach. Econometrica, 59, p. 347-70, 1991.
NELSON, D. B. Stationarity and persistence in the GARCH(1,1) model. Econometric
Theory, 6, p. 318-34, 1990a.
NELSON, D. B. ARCH models as diffusion approximations. Journal ofEconometrics, 45, p. 7-38, 1990b.
NOH, J., ENGLE, R. E & KANE, A. Forecasting volatility and option prices of the S&P 500 index. Journal of Derivatives, p. 17-30, 1994.
PAGAN, A. R. and SCHWERT, G. W Alternative models for conditional stock volatility./owrmr/ ofEconometrics, 45, p. 267-290, 1990.
PORTUGAL, M. S. Neural network versus time series models: a forecasting exercise. Revista Brasileira de Economia, v. 49, p. 611-629, 1995.
RUIZ, E. Quasi maximum lifelihood estimation ofstochastic volatility models. Journal of Econometrics, 63, p. 289-306, 1994.
SENTANA, E. Quadratic ARCH models. Review ofEconomic Studies, 62, p. 639-661, 1995.
ZAKOIAN, J. Michel Threshold heteroskedastic models. Journal of Economic Dynamics and Control, 18, p. 931-955, 1994.
ZIEGELMANN, E A. & PEREIRA, P. L. V Modelos de volatilidade estocastica com deforma^ao temporal: um estudo empirico para o índice
Ibovesa.Pesquisa e PlanejamentoEconomico, v. 27, n. 2, p. 353-376,1997.
Downloads
Published
Issue
Section
License
Copyright (c) 1999 Igor A. C. de Morais, Marcelo S. Portugal
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
By submitting an article, the author authorizes its publication and attests that it has not been submitted to any other journal. The original article is considered final. Articles selected for publication are proofread for grammatical and orthographic errors. The journal does not pay rights for published articles. The Institute of Economic Research from the School of Economics, Business and Accounting of the University of São Paulo (Instituto de Pesquisas Econômicas da Faculdade de Economia, Administração e Contabilidade da Universidade de São Paulo) owns the journal's copyright.
