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Bist 30 Hisse Senetlerinin Gelecekteki Değerlerinin Geometrik Brownıan Hareketi İle Tahmini Ve Arıma, Sarıma, Garch, Egarch, Gjr Modelleri İle Volatilite Analizi

Year 2021, Issue: Özel Sayı 2, 191 - 218, 02.02.2021

Sonat Bayram

https://doi.org/10.33203/mfy.844861

Abstract

Geometrik Brownian Hareketi (GBM) ile BIST 30 hisse senetlerinin gelecek değerlerini tespit etmede, özellikle ilk otuz gündeki isabet oranının oldukça yüksek olduğu, süre uzadıkça dışsal şoklara bağlı olarak tahmin hatasının yükseldiği ve özellikle de düşük varyansa sahip hisse senetlerinin tahmin hatasının diğerlerinden daha düşük olduğu tespit edilmiştir. Geometrik Brownian Hareketi (GBM) ile üretilen zaman serilerinin otoregresif entegre hareketli ortalama mevsimsel ARIMA (SARIMA) (Gaussian Dağılım) modeli ile daha isabetli ölçümlendiği (12 şirket), ardından en iyi asimetri tipi volatilite modelinin sırasıyla EGARCH (11 şirket), GARCH (6 şirket), GJR (1 şirket) olduğu tespit edilmiştir.

Keywords

GBM Volatilite EGARCH GJR

References

  • Alberg, D., Shalit, H., & Yosef, R. (2008). Estimating stock market volatility using asymmetric GARCH models. Applied Financial Economics, 18(15), pp.1201-1208.
  • Bachelier, L. (2011). Louis Bachelier's theory of speculation: the origins of modern finance. Princeton University Press.
  • Bender, C., Sottinen, T., & Valkeila, E. (2007). Arbitrage with fractional Brownian motion?. Theory of Stochastic Processes Vol.13 (29), no.1-2, 2007, pp.23-34
  • Black F, Scholes M (1973) The pricing of options and corporate liabilities, Jounal of Political Economy 81, pp.637–659
  • Bracker, K., & Smith, K. L. (1999). Detecting and modeling changing volatility in the copper futures market. Journal of Futures Markets: Futures, Options, and Other Derivative Products, 19(1), pp.79-100.
  • Chalasani, P., & Jha, S. (1997). Steven Shreve: Stochastic Calculus and Finance. Lecture Notes, October. pp.1-343
  • De Meyer, B., & Saley, H. M. (2003). On the strategic origin of Brownian motion in finance. International Journal of Game Theory, 31(2), pp.285-319
  • Demireli, E., & Hepkorucu, A. (2010). Çevre Finansmanı: Kavramsal Bir Yaklaşımla Karbon Finans Borsası. Ekonomi Bilimleri Dergisi, 2(2), pp.37-48
  • Duan, J., Gauthier, G., Simonato, J., & Sasseville, C. (2006). Approximating the GJR-GARCH and EGARCH option pricing models analytically. Journal of Computational Finance, 9(3), pp.1-41
  • Elliott, R. J., & Van Der Hoek, J. (2001). Fractional Brownian motion and financial modelling. In Mathematical Finance. Birkhäuser, Basel. pp.140-151
  • Hu, Y., & Øksendal, B. (2003). Fractional white noise calculus and applications to finance. Infinite dimensional analysis, quantum probability and related topics, 6(01), pp.1-32 Iglesias, E. M., & Linton, O. (2009). Estimation of tail thickness parameters from GJR-GARCH models. Departamento de Economía Universidad Carlos III de Madrid. Working Paper 09-47 Economic Series (26), pp.1-30
  • İnam, U. (2011). Geometrik Brownian Hareketle Hisse Senedi Fiyatının Gelecek Değerinin Belirlenmesi. Marmara Ünı̇versı̇tesı̇ Sosyal Bı̇lı̇mler Enstı̇tüsü İşletme Anabı̇lı̇m Dalı Sayısal Yöntemler Bı̇lı̇m Dalı, Yayınlanmamış Yüksek Lisans Tezi.
  • İş Yatırım, 2020, https://www.isyatirim.com.tr/tr-tr/analiz/hisse/Sayfalar/Tarihsel-Fiyat-Bilgileri.aspx, (Erişim Tarihi: 26.08.2020)
  • Karanasos, M., & Kim, J. (2003). Moments of the ARMA–EGARCH model. The Econometrics Journal, 6(1), pp.146-166
  • Karatzas, I., & Shreve, S. E. (1998). Brownian motion. In Brownian Motion and Stochastic Calculus (pp. 47-127). Springer, New York, NY
  • Liu, H. C., & Hung, J. C. (2010). Forecasting S&P-100 stock index volatility: The role of volatility asymmetry and distributional assumption in GARCH models. Expert Systems with Applications, 37(7), pp.4928-4934
  • Monfared, S. A., & Enke, D. (2014). Volatility forecasting using a hybrid GJR-GARCH neural network model. Procedia Computer Science, 36, pp.246-253
  • Øksendal, B. (2003). Fractional Brownian motion in finance. Preprint series. Pure mathematics http://urn. nb. no/URN: NBN: no-8076
  • Ou, P., & Wang, H. (2011, July). Modeling and forecasting stock market volatility by Gaussian processes based on GARCH, EGARCH and GJR models. In Proceedings of the World Congress on Engineering. Vol. 1, pp. 6-8
  • Özkan, T., & Güngör, B. (2017). Geometrik Brownıan Hareketi Modeli İle Endeks Dalgalanmalarını Değerlendirme: BIST-30, BIST-100 ve S&P 500 Endeksleri Üzerine Bir Uygulama. Atatürk Üniversitesi İktisadi ve İdari Bilimler Dergisi, Cilt: 31 2017 Sayı: 2, ss.377-395
  • Peters, J. P. (2001). Estimating and forecasting volatility of stock indices using asymmetric GARCH models and (Skewed) Student-t densities. Preprint, University of Liege, Belgium, 3, pp.19-34
  • Rostek, S., & Schöbel, R. (2013). A note on the use of fractional Brownian motion for financial modeling. Economic Modelling, 30, pp.30-35
  • Tseng, F. M., Yu, H. C., & Tzeng, G. H. (2002). Combining neural network model with seasonal time series ARIMA model. Technological forecasting and social change, 69(1), pp.71-87
  • Working, H. (1949). The theory of price of storage. The American Economic Review, 39(6), pp.1254-1262

Year 2021, Issue: Özel Sayı 2, 191 - 218, 02.02.2021

Sonat Bayram

https://doi.org/10.33203/mfy.844861

Abstract

References

  • Alberg, D., Shalit, H., & Yosef, R. (2008). Estimating stock market volatility using asymmetric GARCH models. Applied Financial Economics, 18(15), pp.1201-1208.
  • Bachelier, L. (2011). Louis Bachelier's theory of speculation: the origins of modern finance. Princeton University Press.
  • Bender, C., Sottinen, T., & Valkeila, E. (2007). Arbitrage with fractional Brownian motion?. Theory of Stochastic Processes Vol.13 (29), no.1-2, 2007, pp.23-34
  • Black F, Scholes M (1973) The pricing of options and corporate liabilities, Jounal of Political Economy 81, pp.637–659
  • Bracker, K., & Smith, K. L. (1999). Detecting and modeling changing volatility in the copper futures market. Journal of Futures Markets: Futures, Options, and Other Derivative Products, 19(1), pp.79-100.
  • Chalasani, P., & Jha, S. (1997). Steven Shreve: Stochastic Calculus and Finance. Lecture Notes, October. pp.1-343
  • De Meyer, B., & Saley, H. M. (2003). On the strategic origin of Brownian motion in finance. International Journal of Game Theory, 31(2), pp.285-319
  • Demireli, E., & Hepkorucu, A. (2010). Çevre Finansmanı: Kavramsal Bir Yaklaşımla Karbon Finans Borsası. Ekonomi Bilimleri Dergisi, 2(2), pp.37-48
  • Duan, J., Gauthier, G., Simonato, J., & Sasseville, C. (2006). Approximating the GJR-GARCH and EGARCH option pricing models analytically. Journal of Computational Finance, 9(3), pp.1-41
  • Elliott, R. J., & Van Der Hoek, J. (2001). Fractional Brownian motion and financial modelling. In Mathematical Finance. Birkhäuser, Basel. pp.140-151
  • Hu, Y., & Øksendal, B. (2003). Fractional white noise calculus and applications to finance. Infinite dimensional analysis, quantum probability and related topics, 6(01), pp.1-32 Iglesias, E. M., & Linton, O. (2009). Estimation of tail thickness parameters from GJR-GARCH models. Departamento de Economía Universidad Carlos III de Madrid. Working Paper 09-47 Economic Series (26), pp.1-30
  • İnam, U. (2011). Geometrik Brownian Hareketle Hisse Senedi Fiyatının Gelecek Değerinin Belirlenmesi. Marmara Ünı̇versı̇tesı̇ Sosyal Bı̇lı̇mler Enstı̇tüsü İşletme Anabı̇lı̇m Dalı Sayısal Yöntemler Bı̇lı̇m Dalı, Yayınlanmamış Yüksek Lisans Tezi.
  • İş Yatırım, 2020, https://www.isyatirim.com.tr/tr-tr/analiz/hisse/Sayfalar/Tarihsel-Fiyat-Bilgileri.aspx, (Erişim Tarihi: 26.08.2020)
  • Karanasos, M., & Kim, J. (2003). Moments of the ARMA–EGARCH model. The Econometrics Journal, 6(1), pp.146-166
  • Karatzas, I., & Shreve, S. E. (1998). Brownian motion. In Brownian Motion and Stochastic Calculus (pp. 47-127). Springer, New York, NY
  • Liu, H. C., & Hung, J. C. (2010). Forecasting S&P-100 stock index volatility: The role of volatility asymmetry and distributional assumption in GARCH models. Expert Systems with Applications, 37(7), pp.4928-4934
  • Monfared, S. A., & Enke, D. (2014). Volatility forecasting using a hybrid GJR-GARCH neural network model. Procedia Computer Science, 36, pp.246-253
  • Øksendal, B. (2003). Fractional Brownian motion in finance. Preprint series. Pure mathematics http://urn. nb. no/URN: NBN: no-8076
  • Ou, P., & Wang, H. (2011, July). Modeling and forecasting stock market volatility by Gaussian processes based on GARCH, EGARCH and GJR models. In Proceedings of the World Congress on Engineering. Vol. 1, pp. 6-8
  • Özkan, T., & Güngör, B. (2017). Geometrik Brownıan Hareketi Modeli İle Endeks Dalgalanmalarını Değerlendirme: BIST-30, BIST-100 ve S&P 500 Endeksleri Üzerine Bir Uygulama. Atatürk Üniversitesi İktisadi ve İdari Bilimler Dergisi, Cilt: 31 2017 Sayı: 2, ss.377-395
  • Peters, J. P. (2001). Estimating and forecasting volatility of stock indices using asymmetric GARCH models and (Skewed) Student-t densities. Preprint, University of Liege, Belgium, 3, pp.19-34
  • Rostek, S., & Schöbel, R. (2013). A note on the use of fractional Brownian motion for financial modeling. Economic Modelling, 30, pp.30-35
  • Tseng, F. M., Yu, H. C., & Tzeng, G. H. (2002). Combining neural network model with seasonal time series ARIMA model. Technological forecasting and social change, 69(1), pp.71-87
  • Working, H. (1949). The theory of price of storage. The American Economic Review, 39(6), pp.1254-1262
There are 24 citations in total.

Details

Primary Language Turkish
Subjects Finance
Journal Section Articles
Authors

Sonat Bayram 0000-0001-9885-8707

Publication Date February 2, 2021
Submission Date December 22, 2020
Published in Issue Year 2021 Issue: Özel Sayı 2

Cite

APA Bayram, S. (2021). Bist 30 Hisse Senetlerinin Gelecekteki Değerlerinin Geometrik Brownıan Hareketi İle Tahmini Ve Arıma, Sarıma, Garch, Egarch, Gjr Modelleri İle Volatilite Analizi. Maliye Ve Finans Yazıları(Özel Sayı 2), 191-218. https://doi.org/10.33203/mfy.844861
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