Annals of Finance

, Volume 7, Issue 1, pp 1–29 | Cite as

On the realized volatility of the ECX CO2 emissions 2008 futures contract: distribution, dynamics and forecasting

Research Article

Abstract

This article documents the conditional and unconditional distributions of the realized volatility for the 2008 futures contract in the European climate exchange (ECX), which is valid under the EU emissions trading scheme (EU ETS). Realized volatility measures from naive, kernel-based and subsampling estimators are used to obtain inferences about the distributional and dynamic properties of the ECX emissions futures volatility. The distribution of the daily realized volatility in logarithmic form is shown to be close to normal. The mixture-of-normals hypothesis is strongly rejected, as the returns standardized using daily measures of volatility clearly departs from normality. A simplified HAR-RV model (Corsi in J Financ Econ 7:174–196, 2009) with only a weekly component, which reproduces long memory properties of the series, is then used to model the volatility dynamics. Finally, the predictive accuracy of the HAR-RV model is tested against GARCH specifications using one-step-ahead forecasts, which confirms the HAR-RV superior ability.

Keywords

CO2 price Realized volatility HAR-RV Emissions markets EU ETS Intraday data Forecasting 

JEL Classification

C5 G1 Q4 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aït-Sahalia Y., Mykland P., Zhang L.: How often to sample a continuous-time process in the presence of market microstructure noise. Rev Financ Stud 18, 351–416 (2005)CrossRefGoogle Scholar
  2. Alberola E., Chevallier J.: European carbon prices and banking restrictions: evidence from phase I (2005–2007). Energy J 30, 107–136 (2009)Google Scholar
  3. Alberola E., Chevallier J., Chèze B.: Price drivers and structural breaks in European carbon prices 2005–2007. Energy Policy 36, 787–797 (2008)CrossRefGoogle Scholar
  4. Andersen T.G.: Return volatility and trading volume: an information flow interpretation of stochastic volatility. J Financ 51, 169–204 (1996)CrossRefGoogle Scholar
  5. Andersen T.G., Benzoni L.: Realized volatility. In: Andersen, T.G., Davis, R.A., Kreiß, J.-P., Mikosch, Th. (eds) Handbook of Financial Time Series, Springer, New York (2009)Google Scholar
  6. Andersen T.G., Bollerslev T.: Answering the skeptics: yes, standard volatility models do provide accurate forecasts. Int Econ Rev 39, 885–905 (1998)CrossRefGoogle Scholar
  7. Andersen T.G., Bollerslev T., Diebold F.X.: Roughing it up: including jump components in the measurement, modeling and forecasting of return volatility. Rev Econ Stat 89, 701–720 (2007)CrossRefGoogle Scholar
  8. Andersen T.G., Bollerslev T., Diebold F.X., Ebens H.: The distribution of stock return volatility. J Financ Econ 61, 43–76 (2001)CrossRefGoogle Scholar
  9. Andersen T.G., Bollerslev T., Diebold F.X., Labys P.: The distribution of exchange rate volatility. J Am Stat Assoc 96, 42–55 (2001)CrossRefGoogle Scholar
  10. Andersen T.G., Bollerslev T., Diebold F.X., Labys P.: Modeling and forecasting realized volatility. Econometrica 71, 579–625 (2003)CrossRefGoogle Scholar
  11. Andersen T.G., Bollerslev T., Meddahi N.: Correcting the errors: volatility forecast evaluation using high-frequency data and realized volatilities. Econometrica 73, 279–296 (2005)CrossRefGoogle Scholar
  12. Andreou E., Ghysels E.: Detecting multiple breaks in financial market volatility dynamics. J Appl Econ 17, 579–600 (2002)CrossRefGoogle Scholar
  13. Areal N., Taylor S.J.: The realized volatility of FTSE-100 futures prices. J Futures Mark 22, 627–648 (2002)CrossRefGoogle Scholar
  14. Awartani B., Corradi V., Distaso W.: Testing market microstructure effect with an application to the Dow Jones industrial average stocks. J Bus Econ Stat 27, 251–265 (2009)CrossRefGoogle Scholar
  15. Barndorff-Nielsen O., Shephard N.: Econometric analysis of realized volatility and its use in estimating stochastic volatility models. J Royal Stat Soc Ser B 64, 253–280 (2002)CrossRefGoogle Scholar
  16. Benz, E., Klar, J.: Liquidity and price discovery in the European CO2 futures market: an intraday analysis. Working Paper, Bonn Graduate School of Business (2008)Google Scholar
  17. Benz E., Truck S.: Modeling the price dynamics of CO2 emission allowances. Energy Econ 1, 4–15 (2009)CrossRefGoogle Scholar
  18. Brockwell P.J., Davis R.A.: Time Series: Theory and Methods, Springer Series in Statistics. Springer, New York (1991)Google Scholar
  19. Bunn, D., Fezzi, C.: Interaction of European carbon trading and energy prices. Fondazione Eni Enrico Mattei working paper 123 (2007)Google Scholar
  20. Cai J., Cheung Y.L., Lee R.S.K., Melvin M.: “Once-in-a-generation” yen volatility in 1998: fundamentals, intervention, and order flow. J Int Money Financ 20, 327–347 (2001)CrossRefGoogle Scholar
  21. Cartea, Á., Börger, R.H., Kiesel, R., Schindlmayr, G.: A multivariate commodity analysis and applications to risk management. Birkbeck working papers in economics and finance BWPEF 0709, Birkbeck, University of London (2007)Google Scholar
  22. Chen W.W., Deo R.S.: Power transformations to induce normality and their applications. J Royal Stat Assoc B 66, 117–130 (2004)CrossRefGoogle Scholar
  23. Chevallier J., Ielpo F., Mercier L.: Risk aversion and institutional information disclosure on the European carbon market: a case-study of the 2006 compliance event. Energy Policy 37, 15–28 (2009)CrossRefGoogle Scholar
  24. Clark P.K.: A subordinated stochastic process model with finite variance for speculative prices. Econometrica 41, 135–156 (1973)CrossRefGoogle Scholar
  25. Corsi F.: A simple approximate long-memory model of realized volatility. J Financ Econ 7, 174–196 (2009)Google Scholar
  26. Corsi F., Mittnik S., Pigorsch C., Pigorsch U.: The volatility of realized volatility. Econ Rev 27, 46–78 (2008)CrossRefGoogle Scholar
  27. Dacorogna M.M., Gençay R., Müller U.A., Olsen R.B., Pictet O.V.: An Introduction to High-Frequency Financ. Academic Press, San Diego, CA (2001)Google Scholar
  28. Daskalakis G., Psychoyios D., Markellos R.N.: Modeling CO2 emission allowance prices and derivatives: evidence from the European trading scheme. J Banking Financ 33, 1230–1241 (2009)CrossRefGoogle Scholar
  29. Duong H.N., Kalev P.S.: The Samuelson hypothesis in futures markets: an analysis using intraday data. J Banking Financ 32, 489–500 (2008)CrossRefGoogle Scholar
  30. Fleming, J., Paye, B.S.: High-frequency returns, jumps and the mixture of normals hypothesis. Unpublished manuscript (2005)Google Scholar
  31. Fong W., Wong W.: The modified mixture of distributions model: a revisit. Ann Financ 2, 167–178 (2006)CrossRefGoogle Scholar
  32. Geweke J., Porter-Hudak S.: The estimation and application of long memory time series models. J Time Ser Anal 4, 221–238 (1983)CrossRefGoogle Scholar
  33. Gonçalves, S., Meddahi, N.: Box-Cox transforms for realized volatility. Unpublished manuscript (2008)Google Scholar
  34. Gonçalves S., Meddahi N.: Bootstrapping realized volatility. Econometrica 77, 283–306 (2009)CrossRefGoogle Scholar
  35. Guillaume D.M., Dacorogna M.M., Davé R.R., Müller U.A., Olsen R.B., Pictet O.V.: From the bird’s eye to the microscope: a survey of new stylized facts of the intra-daily foreign exchange markets. Financ Stoch 1, 95–129 (1997)CrossRefGoogle Scholar
  36. Hansen P.R., Lunde A.: Realized variance and market microstructure noise. J Bus Econ Stat 24, 127–218 (2006)CrossRefGoogle Scholar
  37. Hansen P.R., Lunde A.: Consistent ranking of volatility models. J Econ 131, 97–121 (2006)Google Scholar
  38. Illueca M., Lafuente J.A.: new evidence on expiration-day effects using realized volatility: an intraday analysis for the Spanish stock exchange. J Futures Mark 26, 923–938 (2006)CrossRefGoogle Scholar
  39. Jondeau E., Poon S.-H., Rockinger M.: Financial Modeling Under Non-Gaussian Distributions. Springer, Springer (2007)Google Scholar
  40. Liu C., Maheu J.M.: Are there structural breaks in realized volatility?. J Finan Econ 6, 326–360 (2008)Google Scholar
  41. Lin Y.N., Lin A.Y.: Pricing the cost of carbon dioxide emission allowance futures. Rev Futures Mark 16, 1–16 (2007)Google Scholar
  42. Luu C.J., Martens M.: Testing the mixture-of-distributions hypothesis using “realized” volatility. J Futures Mark 23, 661–679 (2003)CrossRefGoogle Scholar
  43. McAleer M., Medeiros M.C.: Realized volatility: a review. Econ Rev 27, 10–45 (2008)CrossRefGoogle Scholar
  44. Müller U.A., Dacorogna M.M., Davé R.D., Olsen R.B., Pictet O.V.: Volatilities of different time resolutions—analyzing the dynamics of market components. J Empir Financ 4, 213–239 (1997)CrossRefGoogle Scholar
  45. Oberndorfer U.: EU emission allowances and the stock market: evidence from the electricity industry. Ecol Econ 68, 1116–1126 (2009)CrossRefGoogle Scholar
  46. Paolella M.S., Taschini L.: An econometric analysis of emission trading allowances. J Banking Financ 32, 2022–2032 (2008)CrossRefGoogle Scholar
  47. Patton, A.J.: Volatility forecast comparison using imperfect volatility proxies. J Econ (2010) (forthcoming)Google Scholar
  48. Patton A.J., Sheppard K.: Optimal combinations of realised volatility estimators. Int J Forecast 25, 218–238 (2009)CrossRefGoogle Scholar
  49. Pong S., Shackleton M.B., Taylor S.J.: Distinguishing short and long memory volatility specifications. Econ J 11, 617–637 (2008)Google Scholar
  50. Tauchen G.E., Pitts M.: The price variability-volume relationship on speculative markets. Econometrica 51, 485–505 (1983)CrossRefGoogle Scholar
  51. Taylor S.J., Xu X.: The incremental volatility information in one million foreign exchange quotations. J Empir Financ 4, 317–340 (1997)CrossRefGoogle Scholar
  52. Thomakos D.D., Wang T.: Realized volatility in the futures markets. J Empir Financ 10, 321–353 (2003)CrossRefGoogle Scholar
  53. Zhang L., Mykland P.A., Aït-Sahalia Y.: A tale of two time scales: determining integrated volatility with noisy high frequency data. J Am Stat Assoc 100, 1394–1411 (2005)CrossRefGoogle Scholar
  54. Zhou B.: High frequency data and volatility in foreign-exchange rates. J Bus Econ Stat 14, 45–52 (1996)CrossRefGoogle Scholar
  55. Zivot, E.: Analysis of High Frequency Financial Data: Models, Methods and Software. University of Washington, Unpublished Manuscript (2005)Google Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Imperial College London (Grantham Institute for Climate Change)University of Paris 10 (EconomiX-CNRS)LondonUK
  2. 2.Faculty of Law, Economics and ManagementUniversity of Angers (GRANEM), LEMNA and Bordeaux Management School (CEREBEM)Angers Cedex 01France

Personalised recommendations