Research ArticleOpen AccessGoogle Scholar indexed
The Long Memory of the Jump Intensity of the Price Process
School of Systems Science, Beijing Normal University, Beijing, China
School of Government, Beijing Normal University, Beijing, China
School of Systems Science, Beijing Normal University, Beijing, China
- 1 School of Systems Science, Beijing Normal University, Beijing, China
- 2 School of Government, Beijing Normal University, Beijing, China
- 3 School of Systems Science, Beijing Normal University, Beijing, China
Journal of Mathematical Finance·Volume 11 (2021)·Pages 176–189·Published 1 March 2021·DOI10.4236/jmf.2021.112009
Copy link · social · email
Abstract
The impact of successive jumps in price process on volatility is very important. We study the nature of self-motivation in price process using data from China’s stock market. Our empirical results suggest that: 1) Price jumps in China’s stock market are generally self-motivated, <i>i.e.</i>, price jumps are clustering. 2) The jump intensity of China’s stock market is time-varying, and follows log-normal distribution, which indicates that the jump intensity is asymmetrical. 3) The jump intensities’ sequence exhibits typical long memory.
KeywordsPrice JumpSelf-MotivatedJump IntensityHurst IndexLong Memory
- Maasoumi, E. and McAleer, M. (2008) Realized Volatility and Long Memory: An Overview. Econometric Reviews, 27, 1-9. https://doi.org/10.1080/07474930701853459
- Kim, S. and Eom, C. (2008) Long-Term Memory and Volatility Clustering in High-Frequency Price Changes. Physica A: Statistical Mechanics and Its Applications, 387, 1247-1254. https://doi.org/10.1016/j.physa.2007.08.061
- Choi, K., Yu, W.-C. and Zivot, E. (2010) Long Memory Versus Structural Breaks in Modeling and Forecasting Realized Volatility. Journal of International Money and Finance, 29, 857-875. https://doi.org/10.1016/j.jimonfin.2009.12.001
- Degiannakis, S. and Floros, C. (2016) Intra-Day Realized Volatility for European and USA Stock Indices. Global Finance Journal, 29, 24-41. https://doi.org/10.1016/j.gfj.2015.05.002
- Merton, R.C. (1976) Option Pricing when Underlying Stock Returns Are Discontinuous. Journal of Financial Economics, 3, 125-144. https://doi.org/10.1016/0304-405X(76)90022-2
- Tankov, P. (2003) Financial Modelling with Jump Processes. CRC Press, New York, 552. https://doi.org/10.1201/9780203485217
- Lee, S.S. and Mykland, P.A. (2008) Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics. The Review of Financial Studies, 21, 2535-2563. https://doi.org/10.1093/rfs/hhm056
- Aït-Sahalia, Y. and Jacod, J. (2009) Estimating the Degree of Activity of Jumps in High Frequency Data. The Annals of Statistics, 37, 2202-2244. https://doi.org/10.1214/08-AOS640
- Aït-Sahalia, Y. and Jacod, J. (2009) Testing for Jumps in a Discretely Observed Process. The Annals of Statistics, 37, 184-222. https://doi.org/10.1214/07-AOS568
- Aït-Sahalia, Y. and Jacod, J. (2011) Testing Whether Jumps have Finite or Infinite Activity. The Annals of Statistics, 39, 1689-1719. https://doi.org/10.1214/11-AOS873
- Aït-Sahalia, Y. and Jacod, J. (2012) Identifying the Successive Blumenthal–Getoor Indices of a Discretely Observed Process. The Annals of Statistics, 40, 1430-1464. https://doi.org/10.1214/12-AOS976
- Aït-Sahalia, Y., Jacod, J. and Li, J. (2012) Testing for Jumps in Noisy High Frequency Data. Journal of Econometrics, 168, 207-222. https://doi.org/10.1016/j.jeconom.2011.12.004
- Todorov, V. and Tauchen, G. (2010) Activity Signature Functions for High-Frequency Data Analysis. Journal of Econometrics, 154, 125-138. https://doi.org/10.1016/j.jeconom.2009.06.009