Hostname: page-component-848d4c4894-v5vhk Total loading time: 0 Render date: 2024-06-19T05:32:56.191Z Has data issue: false hasContentIssue false
  • English
  • Français

Volatility determination in an ambit process setting

Part of: Stochastic processes Stochastic analysis Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

Ole E. Barndorff-Nielsen  and
Svend Erik Graversen
Ole E. Barndorff-Nielsen
Affiliation:
Aarhus University, Thiele Centre, Department of Mathematical Sciences, Aarhus University, Ny Munkegade 118, Building 1530, DK-8000 Aarhus C, Denmark. Email address: oebn@imf.au.dk
Svend Erik Graversen
Affiliation:
Aarhus University, Thiele Centre, Department of Mathematical Sciences, Aarhus University, Ny Munkegade 118, Building 1530, DK-8000 Aarhus C, Denmark. Email address: matseg@imf.au.dk
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The limit behaviour in probability of realised quadratic variation is discussed under a relatively simple ambit process setting. The relation of this to the underlying volatility/intermittency field is in focus, especially as concerns the question of no volatility/intermittency memory.

Keywords

Ambit fieldrealised quadratic variationvolatility memorylessness

MSC classification

Primary: 60G60: Random fields
Secondary: 60H99: None of the above, but in this section 62M30: Spatial processes
Type
Part 6. Statistics
Information
Journal of Applied Probability , Volume 48 , Issue A: New Frontiers in Applied Probability (Journal of Applied Probability Special Volume 48A) , August 2011 , pp. 263 - 275
Copyright
Copyright © Applied Probability Trust 2011 

References

[1] Barndorff-Nielsen, O. E. and Schmiegel, J., (2004). Lévy-based tempo-spatial modelling; with applications to turbulence. Uspekhi Mat. NAUK 59, 65–91.Google Scholar
[2] Barndorff-Nielsen, O. E. and Schmiegel, J., (2007). Ambit processes; with applications to turbulence and cancer growth. In Stochastic Analysis and Applications: The Abel Symposium 2005, eds Benth, F. E. et al., Springer, Berlin, pp. 93–124.Google Scholar
[3] Barndorff-Nielsen, O. E. and Schmiegel, J., (2009). Brownian semistationary processes and volatility/intermittency. In Advanced Financial Modelling (Radon Ser. Comput. Appl. Math. 8), eds Albrecher, H., Rungaldier, W., and Schachermeyer, W., Walter de Gruyter, Berlin, pp. 1–25.Google Scholar
[4] Barndorff-Nielsen, O. E. and Shephard, N., (2004). Econometric analysis of realized covariation: high frequency covariance, regression, and correlation in financial economics. Econometrica 72, 885–925.CrossRefGoogle Scholar
[5] Barndorff-Nielsen, O. E. and Shephard, N., (2004). Power and bipower variation with stochastic volatility and jumps (with discussion). J. Financial Econometrics 2, 1–48.Google Scholar
[6] Barndorff-Nielsen, O. E., Corcuera, J. M. and Podolskij, M., (2011). Multipower variation for Brownian semistationary processes. To appear in Bernoulli.CrossRefGoogle Scholar
[7] Barndorff-Nielsen, O. E.,et al. (2006). A central limit theorem for realised power and bipower variations of continuous semimartingales. In From Stochastic Calculus to Mathematical Finance (Festschrift in Honour of A. N. Shiryaev), eds Kabanov, Y., Lipster, R., and Stoyanov, J., Springer, Berlin, pp. 33–68.CrossRefGoogle Scholar
[8] Dunford, N. and Schwartz, J. T., (1958). Linear Operators. I. General Theory. Interscience, New York.Google Scholar
[9] Hoffmann-Jörgensen, J., (1994). Probability with a View toward Statistics, Vol. II. Chapman and Hall, New York.Google Scholar
[10] Jacod, J., (2008). Asymptotic properties of realized power variations and related functionals of semimartingales. Stoch. Process. Appl. 118, 517–559.Google Scholar