Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics and Decision Sciences
Volume 2006, Article ID 86320, 23 pages
http://dx.doi.org/10.1155/JAMDS/2006/86320

Recent developments in volatility modeling and applications

1Department of Statistics, University of Manitoba, Winnipeg, MB, Canada R3T 2N2
2Department of Supply Chain Management, University of Manitoba, Winnipeg, MB, Canada R3T 2N2
3Department of Business Administration, University of Manitoba, Winnipeg, MB, Canada R3T 2N2

Received 21 February 2006; Revised 10 July 2006; Accepted 24 September 2006

Copyright © 2006 A. Thavaneswaran et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. Abraham and A. Thavaneswaran, “A nonlinear time series model and estimation of missing observations,” Annals of the Institute of Statistical Mathematics, vol. 43, no. 3, pp. 493–504, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. S. S. Appadoo, M. Ghahramani, and A. Thavaneswaran, “Moment properties of some time series models,” The Mathematical Scientist, vol. 30, no. 1, pp. 50–63, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. S. S. Appadoo, A. Thavaneswaran, and J. Singh, “RCA models with correlated errors,” Applied Mathematics Letters, vol. 19, no. 8, pp. 824–829, 2006. View at Publisher · View at Google Scholar
  4. T. Bollerslev, “Generalized autoregressive conditional heteroskedasticity,” Journal of Econometrics, vol. 31, no. 3, pp. 307–327, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. J. C. Duan, G. Gauthier, J. G. Simonato, and C. Sassevillen, “Approximate the GJR-GARCH and EGARCH option pricing models analytically,” Working Paper, University of Toronto, Ontario, 2004. View at Google Scholar
  6. J. C. Duan and J. Wei, “Pricing foreign currency and cross-currency options under GARCH,” Journal of Derivatives, vol. 7, no. 1, pp. 51–63, 1999. View at Google Scholar
  7. R. F. Engle, “Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation,” Econometrica, vol. 50, no. 4, pp. 987–1007, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. R. F. Engle and G. Gonzalez-Rivera, “Semiparametric ARCH models,” Journal of Business and Economic Statistics, vol. 9, no. 4, pp. 345–359, 1991. View at Publisher · View at Google Scholar
  9. P. D. Feigin and R. L. Tweedie, “Random coefficient autoregressive processes: a Markov chain analysis of stationarity and finiteness of moments,” Journal of Time Series Analysis, vol. 6, no. 1, pp. 1–14, 1985. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. F. Fornari and A. Mele, “Sign- and volatility-switching ARCH models: theory and applications to international stock markets,” Journal of Applied Econometrics, vol. 12, no. 1, pp. 49–65, 1997. View at Publisher · View at Google Scholar
  11. M. Ghahramani and A. Thavaneswaran, “Identification of ARMA models with GARCH errors,” Mathematical Scientist, vol. 32, no. 1, 2007, in preparation. View at Google Scholar
  12. C. Gouriéroux, ARCH Models and Financial Applications, Springer Series in Statistics, Springer, New York, 1997. View at Zentralblatt MATH · View at MathSciNet
  13. C. W. J. Granger, “Overview of nonlinear time series specification in economics,” in National Science Foundation Summer Symposia on Econometrics and Statistics, California, 1998.
  14. C. W. J. Granger and T. Teräsvirta, “A simple nonlinear time series model with misleading linear properties,” Economics Letters, vol. 62, no. 2, pp. 161–165, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. C. He and T. Teräsvirta, “Properties of moments of a family of GARCH processes,” Journal of Econometrics, vol. 92, no. 1, pp. 173–192, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. S. L. Heston, “A closed-form solution for options with stochastic volatility with applications to bond and currency options,” Review of Financial Studies, vol. 6, no. 2, pp. 327–343, 1993. View at Publisher · View at Google Scholar
  17. S. L. Heston and S. Nandi, “A closed-form GARCH option valuation model,” Review of Financial Studies, vol. 13, no. 3, pp. 585–625, 2000. View at Publisher · View at Google Scholar
  18. R. Leipus and D. Surgailis, “Random coefficient autoregression, regime switching and long memory,” Advances in Applied Probability, vol. 35, no. 3, pp. 737–754, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. D. F. Nicholls and B. G. Quinn, Random Coefficient Autoregressive Models: An Introduction, vol. 11 of Lecture Notes in Statistics, Springer, New York, 1982. View at Zentralblatt MATH · View at MathSciNet
  20. A. Thavaneswaran and B. Abraham, “Estimation for nonlinear time series models using estimating equations,” Journal of Time Series Analysis, vol. 9, no. 1, pp. 99–108, 1988. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. A. Thavaneswaran, S. S. Appadoo, and S. Peiris, “Forecasting volatility,” Statistics & Probability Letters, vol. 75, no. 1, pp. 1–10, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. A. Thavaneswaran, S. S. Appadoo, and M. Samanta, “Random coefficient GARCH models,” Mathematical and Computer Modelling, vol. 41, no. 6-7, pp. 723–733, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. A. Thavaneswaran and C. C. Heyde, “Prediction via estimating functions,” Journal of Statistical Planning and Inference, vol. 77, no. 1, pp. 89–101, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. A. Timmermann, “Moments of Markov switching models,” Journal of Econometrics, vol. 96, no. 1, pp. 75–111, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet