PL EN


2011 | 7 (14) | 93-106
Article title

The normality of financial data after an extraction of jumps in the jump-diffusion model

Authors
Content
Title variants
Languages of publication
EN
Abstracts
EN
When modelling financial data the jump-diffusion processes, driven by Wiener (W) and Poisson (N) processes, gain increasing importance. On the one hand, they explain better than the Itô diffusion the heavy tails of distributions of percentage changes of stock prices; on the other hand, unlike for example α-stable processes, they are based on the well developed mathematical tools for the Wiener and Poisson processes. After the identification of the jump times, e.g. by means of one of the so-called threshold methods, which are not linked with the continuous part of the model, the parameters from the continuous terms may be estimated similarly as for the Itô diffusion. But it is not obvious if the financial data after an extraction of jumps are already normally distributed. Therefore results of several normality tests will be presented here for chosen data from the Polish stock exchange market.
Year
Issue
Pages
93-106
Physical description
Contributors
References
  • Andersen T., Bollerslev T., Diebold F. (2007). Roughing it up: Including jump components in the measurement, modeling and forecasting of return volatility. Review of Economics and Statistics. Vol. 89. Pp. 701-720.
  • Bandi F., Nguyen T. (2003). On the functional estimation of jump-diffusion models. Journal of Econometrics. Vol. 116. Pp. 293-328.
  • Barndorff-Nielsen O.E., Shephard N. (2006). Econometrics of testing for jumps in financial economics using bipower variation. Journal of Financial Econometrics. Vol. 4. Pp. 1-30.
  • Cont R., Tankov P. (2004). Financial Modelling with Jump Processes. Chapman & Hall – CRC.
  • Das S. (2002). The surprise element: Jumps in interest rates. Journal of Econometrics. Vol. 106. Pp. 27-65.
  • Gardoń A. (2004). The order of approximations for solutions of it ô-type stochastic differential equations with jumps. Stochastic Analysis and Applications. Vol. 22. No. 3. Pp. 679-699.
  • Gardoń A. (2006). The order 1.5 approximations for solutions of jump-diffusion equations. Stochastic Analysis and Applications. Vol. 24. No. 6. Pp. 1147-1168.
  • Gardoń A. (2010). The identification of discontinuities for the jump-diffusion process by means of a modified threshold method. In: Proceedings of the International Scientific Conference AMSE 2010, Demänovská Dolina, Slovakia, 26-29 August 2010, Pp. 105-114
  • Glasserman P., Merener M. (2003). Numerical solution of jump-diffusion LIBOR market models. Finance and Stochastics. Vol. 7. Pp. 1-27.
  • Johannes M. (2004). The statistical and economic role of jumps in continuous-time interest rate models. Journal of Finance. Vol. 59. Pp. 227-260.
  • Karatzas I., Shreve S.E. (1998). Methods of Mathematical Finance. Springer-Verlag. New York.
  • Kloeden P.E., Platen E. (1995). Numerical Solution of Stochastic Differential Equations. Springer-Verlag. New York–Berlin–Heidelberg.
  • Mancini C. (2004). Estimation of the parameters of jump of a general poissondiffusion model. Scandinavian Actuarial Journal. Vol. 1. Pp. 42-52.
  • Mancini C. (2009). Non parametric threshold estimation for models with stochastic diffusion coefficient and jumps. Scandinavian Journal of Statistics. Vol. 36. Issue 2. Pp. 270-296.
  • Ogihara T., Yoshida N. (2011). Quasi-likelihood analysis for the stochastic differential equation with jumps. Statistical Inference for Stochastic Processes. Vol. 14. Pp. 189-229.
  • Peiró A. (1999). Skewness in financial returns. Journal of Banking and Finance. Vol. 23. Issue 6. Pp. 847-862.
  • Shimizu Y., Yoshida N. (2006). Estimation of parameters for diffusion processes with jumps from discrete observations. Statistical Inference for Stochastic Processes. Vol. 9. Pp. 227-277.
  • Sobczyk K. (1991). Stochastic Differential Equations with Applications to Physics and Engineering. Kluwer Academic Publishers B.V. Dordrecht.
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.desklight-61763902-3278-4fe1-a15f-70011132eee3
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.