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No-Arbitrage Semi-Martingale Restrictions for Continuous-Time Volatility Models subject to Leverage Effects, Jumps and i.i.d. Noise: Theory and Testable Distributional Implications

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  • Torben G. Andersen
  • Tim Bollerslev
  • Dobrislav Dobrev

Abstract

We develop a sequential procedure to test the adequacy of jump-diffusion models for return distributions. We rely on intraday data and nonparametric volatility measures, along with a new jump detection technique and appropriate conditional moment tests, for assessing the import of jumps and leverage effects. A novel robust-to-jumps approach is utilized to alleviate microstructure frictions for realized volatility estimation. Size and power of the procedure are explored through Monte Carlo methods. Our empirical findings support the jump-diffusive representation for S&P500 futures returns but reveal it is critical to account for leverage effects and jumps to maintain the underlying semi-martingale assumption.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 12963.

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Date of creation: Mar 2007
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Publication status: published as Andersen, Torben G. & Bollerslev, Tim & Dobrev, Dobrislav, 2007. "No-arbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects, jumps and i.i.d. noise: Theory and testable distributional implications," Journal of Econometrics, Elsevier, vol. 138(1), pages 125-180, May.
Handle: RePEc:nbr:nberwo:12963

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  1. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, MIT Press, vol. 69(3), pages 542-47, August.
  2. 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, MIT Press, vol. 89(4), pages 701-720, November.
  3. Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Vega, Clara, 2002. "Micro Effects of Macro Announcements: Real-Time Price Discovery in Foreign Exchange," Working Papers, University of Pennsylvania, Wharton School, Weiss Center 02-1, University of Pennsylvania, Wharton School, Weiss Center.
  4. Yacine Aït-Sahalia, 2005. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 18(2), pages 351-416.
  5. Andersen, Torben G, 1996. " Return Volatility and Trading Volume: An Information Flow Interpretation of Stochastic Volatility," Journal of Finance, American Finance Association, American Finance Association, vol. 51(1), pages 169-204, March.
  6. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Clara Vega, 2005. "Real-Time Price Discovery in Stock, Bond and Foreign Exchange Markets," NBER Working Papers, National Bureau of Economic Research, Inc 11312, National Bureau of Economic Research, Inc.
  7. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 13(3), pages 345-382.
  8. Geert Bekaert & Guojun Wu, 1997. "Asymmetric Volatility and Risk in Equity Markets," NBER Working Papers, National Bureau of Economic Research, Inc 6022, National Bureau of Economic Research, Inc.
  9. Laszlo Gillemot & J. Doyne Farmer & Fabrizio Lillo, 2006. "There's more to volatility than volume," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 6(5), pages 371-384.
  10. Fulvio Corsi & Gilles Zumbach & Ulrich Müller & Michel Dacorogna, 2004. "Consistent high-precision volatility from high-frequency data," Finance, EconWPA 0407005, EconWPA.
  11. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
  12. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2005. "Correcting the Errors: Volatility Forecast Evaluation Using High-Frequency Data and Realized Volatilities," Econometrica, Econometric Society, Econometric Society, vol. 73(1), pages 279-296, 01.
  13. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, Elsevier, vol. 108(2), pages 281-316, June.
  14. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, Elsevier, vol. 45(1-2), pages 7-38.
  15. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous-time stochastic volatility models," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 8(4), pages 291-323.
  16. 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.
  17. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers, National Bureau of Economic Research, Inc 8160, National Bureau of Economic Research, Inc.
  18. Meddahi, N., 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 2001-26, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  19. 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.
  20. Ole E. Barndorff-Nielsen & Neil Shephard, 2002. "Estimating quadratic variation using realized variance," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 17(5), pages 457-477.
  21. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range-Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, American Finance Association, vol. 57(3), pages 1047-1091, 06.
  22. 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.
  23. Oomen, Roel C.A., 2006. "Properties of Realized Variance Under Alternative Sampling Schemes," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 24, pages 219-237, April.
  24. Bollen, Bernard & Inder, Brett, 2002. "Estimating daily volatility in financial markets utilizing intraday data," Journal of Empirical Finance, Elsevier, Elsevier, vol. 9(5), pages 551-562, December.
  25. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers, Massachusetts Institute of Technology (MIT), Sloan School of Management 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  26. Christian Bontemps & Nour Meddahi, 2002. "Testing Normality: A GMM Approach," CIRANO Working Papers, CIRANO 2002s-63, CIRANO.
  27. Drost, F.C. & Nijman, T.E. & Werker, B.J.M., 1994. "Estimation and testing in models containing both jumps and conditional heteroskedasticity," Discussion Paper, Tilburg University, Center for Economic Research 1994-105, Tilburg University, Center for Economic Research.
  28. Nelson, Daniel B., 1992. "Filtering and forecasting with misspecified ARCH models I : Getting the right variance with the wrong model," Journal of Econometrics, Elsevier, Elsevier, vol. 52(1-2), pages 61-90.
  29. Hansen, Peter R. & Lunde, Asger, 2006. "Realized Variance and Market Microstructure Noise," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 24, pages 127-161, April.
  30. Harris, Lawrence, 1986. "A transaction data study of weekly and intradaily patterns in stock returns," Journal of Financial Economics, Elsevier, Elsevier, vol. 16(1), pages 99-117, May.
  31. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 347-70, March.
  32. Bjørn Eraker, 2004. "Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices," Journal of Finance, American Finance Association, American Finance Association, vol. 59(3), pages 1367-1404, 06.
  33. John M. Maheu & Thomas H. McCurdy, 2004. "News Arrival, Jump Dynamics, and Volatility Components for Individual Stock Returns," Journal of Finance, American Finance Association, American Finance Association, vol. 59(2), pages 755-793, 04.
  34. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, Econometric Society, vol. 41(1), pages 135-55, January.
  35. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, Elsevier, vol. 61(1), pages 43-76, July.
  36. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 53(1), pages 61-65, January.
  37. Lars Forsberg & Tim Bollerslev, 2002. "Bridging the gap between the distribution of realized (ECU) volatility and ARCH modelling (of the Euro): the GARCH-NIG model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 17(5), pages 535-548.
  38. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2002. "Analytic Evaluation of Volatility Forecasts," CIRANO Working Papers, CIRANO 2002s-90, CIRANO.
  39. Wood, Robert A & McInish, Thomas H & Ord, J Keith, 1985. " An Investigation of Transactions Data for NYSE Stocks," Journal of Finance, American Finance Association, American Finance Association, vol. 40(3), pages 723-39, July.
  40. 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.
  41. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
  42. Ole E. Barndorff-Nielsen & Neil Shephard, 2003. "Power and bipower variation with stochastic volatility and jumps," Economics Papers, Economics Group, Nuffield College, University of Oxford 2003-W17, Economics Group, Nuffield College, University of Oxford.
  43. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, Royal Statistical Society, vol. 63(2), pages 167-241.
  44. Zhou, Bin, 1996. "High-Frequency Data and Volatility in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 14(1), pages 45-52, January.
  45. Mikhail Chernov & A. Ronald Gallant & Eric Ghysels & George Tauchen, 2002. "Alternative Models for Stock Price Dynamics," CIRANO Working Papers, CIRANO 2002s-58, CIRANO.
  46. Chan, Wing H & Maheu, John M, 2002. "Conditional Jump Dynamics in Stock Market Returns," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(3), pages 377-89, July.
  47. A. Ronald Gallant & Chien-Te Hsu & George Tauchen, 1999. "Using Daily Range Data To Calibrate Volatility Diffusions And Extract The Forward Integrated Variance," The Review of Economics and Statistics, MIT Press, MIT Press, vol. 81(4), pages 617-631, November.
  48. Xin Huang & George Tauchen, 2005. "The Relative Contribution of Jumps to Total Price Variance," Journal of Financial Econometrics, Society for Financial Econometrics, Society for Financial Econometrics, vol. 3(4), pages 456-499.
  49. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, Elsevier, vol. 94(1-2), pages 181-238.
  50. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, Elsevier, vol. 63(1), pages 3-50, January.
  51. 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, Econometric Society, vol. 44(2), pages 305-21, March.
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