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Aggregation and Model Construction for Volatility Models

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  • Barndorf-Nielsen, O.E.
  • Shephard, N.

Abstract

In this paper we will rigourously study some of the properties of continuous time stochastic volatility models. We have five main results, including: the stochastic volatility class can be linked to Cox process based models of tick-by-tick financial data; we characterise the moments, autocorrelation function and spectrum of squared returns; based only on discrete time returns, we give a simple consistent and asymptotically normally distributed estimator of continuous time volatility models without any simulation or discretisation error.

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Bibliographic Info

Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 141.

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Length: 36 pages
Date of creation: 1998
Date of revision:
Handle: RePEc:nuf:econwp:141

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Web page: http://www.nuff.ox.ac.uk/economics/

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Keywords: MODELS;

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References

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  1. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, Elsevier, vol. 45(1-2), pages 239-265.
  2. Drost, F.C. & Nijman, T.E., 1990. "Temporal aggregation of GARCH processes," Discussion Paper, Tilburg University, Center for Economic Research 1990-66, Tilburg University, Center for Economic Research.
  3. Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, Econometric Society, vol. 51(2), pages 485-505, March.
  4. Torben G. Andersen & Tim Bollerslev, 1996. "Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns," NBER Working Papers 5752, National Bureau of Economic Research, Inc.
  5. Mervyn King & Enrique Sentana & Sushil Wadhwani, 1990. "Volatiltiy and Links Between National Stock Markets," NBER Working Papers 3357, National Bureau of Economic Research, Inc.
  6. Smith, A A, Jr, 1993. "Estimating Nonlinear Time-Series Models Using Simulated Vector Autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 8(S), pages S63-84, Suppl. De.
  7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 31(3), pages 307-327, April.
  8. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, American Finance Association, vol. 42(2), pages 281-300, June.
  9. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 12(04), pages 657-681, October.
  10. Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 65(3), pages 361-93, July.
  11. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
  12. Werker, B.J.M. & Drost, F.C., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Open Access publications from Tilburg University, Tilburg University urn:nbn:nl:ui:12-72561, Tilburg University.
  13. Gennotte, Gerard & Marsh, Terry A., 1993. "Variations in economic uncertainty and risk premiums on capital assets," European Economic Review, Elsevier, Elsevier, vol. 37(5), pages 1021-1041, June.
  14. Diebold, Francis X & Nerlove, Marc, 1989. "The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor Arch Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 4(1), pages 1-21, Jan.-Mar..
  15. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  16. Rice, John, 1979. "On the estimation of the parameters of a power spectrum," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 9(3), pages 378-392, September.
  17. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, Econometric Society, vol. 53(2), pages 385-407, March.
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Cited by:
  1. Torben Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," NBER Working Papers 6961, National Bureau of Economic Research, Inc.
  2. John M. Maheu & Thomas H. McCurdy, 2001. "Nonlinear Features of Realized FX Volatility," CIRANO Working Papers, CIRANO 2001s-42, CIRANO.
  3. Yue Fang, 2000. "When Should Time be Continuous? Volatility Modeling and Estimation of High-Frequency Data," Econometric Society World Congress 2000 Contributed Papers, Econometric Society 0843, Econometric Society.
  4. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2000. "Exchange Rate Returns Standardized by Realized Volatility are (Nearly) Gaussian," NBER Working Papers 7488, National Bureau of Economic Research, Inc.
  5. Stavros Degiannakis & Evdokia Xekalaki, 2007. "Assessing the performance of a prediction error criterion model selection algorithm in the context of ARCH models," Applied Financial Economics, Taylor & Francis Journals, Taylor & Francis Journals, vol. 17(2), pages 149-171.

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