A functional central limit theorem for the realized power variation of integrated stable processes

Stochastic Analysis and Applications

Volumn 25, Issue 1, 2007, Pages 169-186

  Corcuera, José Manuel ^a   Nualart, David ^b   Woerner, Jeannette H C ^c  

^a UNIVERSITY OF BARCELONA   (Spain)

^b UNIVERSITY OF KANSAS   (United States)

^c UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

Central limit theorem; P variation; Realized power variation; Stable processes; Young inequality

Indexed keywords

EID: 33845439129     PISSN: 07362994     EISSN: 15329356     Source Type: Journal    
DOI: 10.1080/07362990601052201     Document Type: Article

References (25)

1. Aldous, D.J., and Eagleson, G.K. 1978. On mixing and stability of limit theorems. The Annals of Probability 6(2):325-331.
2. Barndorff-Nielsen, O.E., and Shephard, N. 2003. Realized power variation and stochastic volatility models. Bernoulli 9(2):243-265.
3. Barndorff-Nielsen, O.E., Graversen, S.E., Jacod, J., Podolskij, M., and Shephard, N. 2005. A central limit theorem for realised power and bipower variations of continuous semimartingales. In From Stochastic Analysis to Mathematical Finance; Festschrift for Albert Shiryaev, Kabanov, Y., Lipster, R., and Stoyanov, J. (Eds.), Springer-Verlag, Berlin, pp. 33-38.
4. Barndorff-Nielsen, O.E., and Shephard, N. 2006. Power variation and time change. Theory of Probability and Its Applications. 50(1):1-15.
5. Billingsley, P. 1968. Convergence of Probability Measures. Wiley and Sons, New York.
6. Bretagnolle, J. 1972. p-variation de fonctions aléatoires. In Séminaire de Probabilités VI, Lecture Notes in Mathematics, 258. Springer, Berlin: pp. 51-71.
7. Carr, P., and Wu, L. 2003. The finite moment logstable process and option pricing. The Journal of Finance 58(2):753-777.
8. Cartea, A., and Howison, S. 2004. Option pricing with Lévy-Stable processes. 2004-MF-01. Working Paper Series in Mathematical Finance, University of Oxford.
9. Corcuera, J.M., Nualart, D., and Woerner, J.H.C. 2005. Power variation of some integral fractional processes. Bernoulli 12(4):713-735.
10. Cont, R., and Tankov, P. 2004. Financial Modelling with Jump Processes. Chapman and Hall, New York.
11. Dudley, R.M., and Norvaiša, R. 1999. Product integrals, young integrals and p-variation. In Differentiability of Six Operators and Nonsmooth Functions and p-variation and Young Integrals. Dudley, R.M. and Norvaiša, R. (Eds.) Lecture Notes in Math. 1703. Springer-Verlag, New York, pp. 73-208.
12. Hudson, W.N., and Mason, J.D. 1976. Variational sums for additive processes. Proc. Amer. Math. Soc. 55:395-399.
13. Hurst, S.R., Platen, E., and Rachev, S.T. 1999. Option pricing for a logstable asset price model. Mathematical and Computer Modelling 29:105-119.
14. Jacod, J. 2005. Asymptotic properties of power variations of Lévy processes. Preprint.
15. Jacod, J. 2006. Asymptotic properties of realized power variations and related functionals of semimartingales. Preprint.
16. Klüppelberg, C., Lindner, A., and Maller, R. 2004. A continuous-time GARCH process driven by a Lévy process: stationary and second-order behaviour. J. Appl. Prob. 41:601-622.
17. Lepingle, D. 1976. La variation d'ordre p des semi-martingales. Z. Wahrscheinlichkeitstheorie verw. Gebiete 36:295-316.
18. McCulloch, J.H. 2003. The risk-neutral measure and option pricing under log-stable uncertainty. Preprint of Economics Department, Ohio State University.
19. Sato, K. 1999. Lévy Processes and Infinitely Divisible Distributions. Cambridge Studies in Advanced Mathematics 68. Cambridge University Press, Cambridge.
20. Schoutens, W. 2003. Lévy Processes in Finance: Pricing Financial Derivatives. John Wiley, Chichester.
21. Shiryaev, A.N. 1999. Essentials of Stochastic Finance. World Scientific, Singapore.
22. Woerner, J.H.C. 2003a. Variational sums and power variation: a unifying approach to model selection and estimation in semimartingale models. Statistics & Decisions 21:47-68.
23. Woerner, J.H.C. 2003b. Purely discontinuous Levy processes and power variation: inference for stochastic volatility and the scale parameter. 2003-MF-08. Working Paper Series in Mathematical Finance, University of Oxford.
24. Woerner, J.H.C. 2005. Estimation of integrated volatility in stochastic volatility models. Applied Stochastic Models in Business and Industry 21:27-44.
25. Young, L.C. 1936. An inequality of the Hölder type connected with Stieltjes integration. Acta Math. 67:251-282.