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Disentangling Volatility from Jumps

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  • Yacine Ait-Sahalia

Abstract

Realistic models for financial asset prices used in portfolio choice, option pricing or risk management include both a continuous Brownian and a jump components. This paper studies our ability to distinguish one from the other. I find that, surprisingly, it is possible to perfectly disentangle Brownian noise from jumps. This is true even if, unlike the usual Poisson jumps, the jump process exhibits an infinite number of small jumps in any finite time interval, which ought to be harder to distinguish from Brownian noise, itself made up of many small moves.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 9915.

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Date of creation: Aug 2003
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Publication status: published as Journal of Financial Economics, 2004, vol. 74, pp. 487-528
Handle: RePEc:nbr:nberwo:9915

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  1. Ernst Eberlein & Sebastian Raible, 1999. "Term Structure Models Driven by General Lévy Processes," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(1), pages 31-53.
  2. Yacine Ait--Sahalia & Per A. Mykland, 2003. "The Effects of Random and Discrete Sampling when Estimating Continuous--Time Diffusions," Econometrica, Econometric Society, Econometric Society, vol. 71(2), pages 483-549, March.
  3. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 75(2), pages 305-332, April.
  4. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, Elsevier, vol. 116(1-2), pages 225-257.
  5. Yacine Ait-Sahalia & Per A. Mykland, 2003. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," NBER Working Papers 9611, National Bureau of Economic Research, Inc.
  6. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, Econometric Society, vol. 71(2), pages 579-625, March.
  7. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, Elsevier, vol. 4(2-3), pages 115-158, June.
  8. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 71(3), pages 371-405, July.
  9. Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, Econometric Society, vol. 70(1), pages 223-262, January.
  10. Ball, Clifford A. & Torous, Walter N., 1983. "A Simplified Jump Process for Common Stock Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 18(01), pages 53-65, March.
  11. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, Elsevier, vol. 1(1), pages 83-106, June.
  12. Beckers, Stan, 1981. "A Note on Estimating the Parameters of the Diffusion-Jump Model of Stock Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 16(01), pages 127-140, March.
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Cited by:
  1. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 701-720, November.
  2. Andersen, Torben G. & Bollerslev, Tim & Francis X. Diebold,, 2003. "Some Like it Smooth, and Some Like it Rough: Untangling Continuous and Jump Components in Measuring, Modeling, and Forecasting Asset Return Volatility," CFS Working Paper Series 2003/35, Center for Financial Studies (CFS).

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