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Original Articles

A Functional Central Limit Theorem for the Realized Power Variation of Integrated Stable Processes

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Pages 169-186 | Received 20 Jul 2006, Accepted 01 Sep 2006, Published online: 15 Dec 2006

REFERENCES

  • Aldous , D.J. , and Eagleson , G.K. 1978 . On mixing and stability of limit theorems . The Annals of Probability 6 ( 2 ): 325 – 331 . [CSA]
  • Barndorff-Nielsen , O.E. , and Shephard , N. 2003 . Realized power variation and stochastic volatility models . Bernoulli 9 ( 2 ): 243 – 265 . [CSA]
  • 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.
  • Barndorff-Nielsen , O.E. , and Shephard , N. 2006 . Power variation and time change . Theory of Probability and Its Applications . 50(1): 1 – 15 . [CSA]
  • Billingsley , P. 1968 . Convergence of Probability Measures . Wiley and Sons , New York .
  • Bretagnolle , J. 1972 . p-variation de fonctions aléatoires . In Séminaire de Probabilités VI , Lecture Notes in Mathematics, 258 . Springer , Berlin : pp. 51 – 71 .
  • Carr , P. , and Wu , L. 2003 . The finite moment logstable process and option pricing . The Journal of Finance 58 ( 2 ): 753 – 777 . [CSA] [CROSSREF]
  • Cartea , A. , and Howison , S. 2004 . Option pricing with Lévy-Stable processes . 2004-MF-01. Working Paper Series in Mathematical Finance , University of Oxford .
  • Corcuera , J.M. , Nualart , D. , and Woerner , J.H.C. 2005 . Power variation of some integral fractional processes . Bernoulli 12 ( 4 ): 713 – 735 . [CSA]
  • Cont , R. , and Tankov , P. 2004 . Financial Modelling with Jump Processes . Chapman and Hall , New York .
  • 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 .
  • Hudson , W.N. , and Mason , J.D. 1976 . Variational sums for additive processes . Proc. Amer. Math. Soc. 55 : 395 – 399 . [CSA] [CROSSREF]
  • 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 . [CSA] [CROSSREF]
  • Jacod , J. 2005 . Asymptotic properties of power variations of Lévy processes . Preprint . [CSA]
  • Jacod , J. 2006 . Asymptotic properties of realized power variations and related functionals of semimartingales . Preprint . [CSA]
  • 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 . [CSA] [CROSSREF]
  • Lepingle , D. 1976 . La variation d'ordre p des semi-martingales . Z. Wahrscheinlichkeitstheorie verw. Gebiete 36 : 295 – 316 . [CSA] [CROSSREF]
  • McCulloch , J.H. 2003 . The risk-neutral measure and option pricing under log-stable uncertainty . Preprint of Economics Department , Ohio State University .
  • Sato , K. 1999 . Lévy Processes and Infinitely Divisible Distributions . Cambridge Studies in Advanced Mathematics 68 . Cambridge University Press , Cambridge .
  • Schoutens , W. 2003 . Lévy Processes in Finance: Pricing Financial Derivatives . John Wiley , Chichester .
  • Shiryaev , A.N. 1999 . Essentials of Stochastic Finance . World Scientific , Singapore .
  • 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. [INFOTRIEVE] [CSA] [CROSSREF]
  • Woerner , J.H.C. 2003b . Purely discontinuous Lévy processes and power variation: inference for stochastic volatility and the scale parameter . 2003-MF-08. Working Paper Series in Mathematical Finance , University of Oxford .
  • Woerner , J.H.C. 2005 . Estimation of integrated volatility in stochastic volatility models . Applied Stochastic Models in Business and Industry 21 : 27 – 44 . [CSA] [CROSSREF]
  • Young , L.C. 1936 . An inequality of the Hölder type connected with Stieltjes integration . Acta Math. 67 : 251 – 282 . [CSA] [CROSSREF]

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