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Basics of Levy processes

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  • Ole E. Barndorff-Nielsen

    ()
    (The T.N. Thiele Centre for Mathematics in Natural Science, Department of Mathematical Sciences, University of Aarhus, Denmark)

  • Neil Shephard

    ()
    (Nuffield College, Dept of Economics and Oxford-Man Institute of Quantitative Finance, University of Oxford.)

Abstract

This is a draft Chapter from a book by the authors on “L´evy Driven Volatility Models”.

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File URL: http://www.nuffield.ox.ac.uk/economics/papers/2012/introlevy120608.pdf
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Bibliographic Info

Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2012-W06.

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Length: 70 pages
Date of creation: 09 Jun 2012
Date of revision:
Handle: RePEc:nuf:econwp:1206

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

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References

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  1. Ole E. Barndorff-Nielsen & Karsten Prause, 2001. "Apparent scaling," Finance and Stochastics, Springer, vol. 5(1), pages 103-113.
  2. Tina Hviid Rydberg, 1997. "A note on the existence of unique equivalent martingale measures in a Markovian setting," Finance and Stochastics, Springer, vol. 1(3), pages 251-257.
  3. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-24, October.
  4. Bauwens, Luc & Laurent, Sebastien, 2005. "A New Class of Multivariate Skew Densities, With Application to Generalized Autoregressive Conditional Heteroscedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 346-354, July.
  5. O. E. Barndorff-Nielsen & S. Z. Levendorskii, 2001. "Feller processes of normal inverse Gaussian type," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 318-331.
  6. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
  7. Ernst Eberlein & Jean Jacod & Sebastian Raible, 2005. "Lévy term structure models: No-arbitrage and completeness," Finance and Stochastics, Springer, vol. 9(1), pages 67-88, January.
  8. M. C. Jones & M. J. Faddy, 2003. "A skew extension of the "t"-distribution, with applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 159-174.
  9. C. W. J. GRANGER & Zhuanxin DING, 1995. "Some Properties of Absolute Return: An Alternative Measure of Risk," Annales d'Economie et de Statistique, ENSAE, issue 40, pages 67-91.
  10. Epps, Thomas W & Epps, Mary Lee, 1976. "The Stochastic Dependence of Security Price Changes and Transaction Volumes: Implications for the Mixture-of-Distributions Hypothesis," Econometrica, Econometric Society, vol. 44(2), pages 305-21, March.
  11. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  12. Ernst Eberlein & Sebastian Raible, 1999. "Term Structure Models Driven by General Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 9(1), pages 31-53.
  13. Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, vol. 51(2), pages 485-505, March.
  14. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-80, April.
  15. Bauer, Christian, 2000. "Value at risk using hyperbolic distributions," Journal of Economics and Business, Elsevier, vol. 52(5), pages 455-467.
  16. 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, vol. 71(3), pages 371-405, July.
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