Computational Economics

, Volume 41, Issue 3, pp 359–386 | Cite as

The Forecasting Performance of Corridor Implied Volatility in the Italian Market

  • Silvia Muzzioli


Corridor implied volatility introduced in Carr and Madan (Volatility: new estimation techniques for pricing derivatives, 1998) and recently implemented in Andersen and Bondarenko (Volatility as an asset class, 2007) is obtained from model-free implied volatility by truncating the integration domain between two barriers. Corridor implied volatility is implicitly linked with the concept that the tails of the risk-neutral distribution are estimated with less precision than central values, due to the lack of liquid options for very high and very low strikes. However, there is no golden choice for the barrier levels, which are likely to change depending on the underlying asset risk neutral distribution. The latter feature renders its forecasting performance mainly an empirical question. The aim of the paper is to investigate the forecasting performance of corridor implied volatility by choosing different corridors with symmetric and asymmetric cuts, and compare the results with the preliminary findings in Muzzioli (CEFIN working paper no 23, 2010b). Moreover, we shed light on the information content of different parts of the risk neutral distribution of the stock price, by using a model-independent approach based on corridor measures. To this end we compute both realized and model-free variance measures accounting for both falls and increases in the underlying asset price. The forecasting performance of volatility measures is evaluated both in a statistical and an economic setting. The economic significance is assessed by employing trading strategies based on delta-neutral straddles. The comparison is pursued by using intra-day synchronous prices between the options and the underlying asset.


Corridor implied volatility Model-free implied volatility Variance swap Corridor variance swap 

JEL Classification

G13 G14 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Ait-Sahalia Y., Lo A. W. (1998) Nonparametric estimation of state-price densities implicit in financial asset prices. Journal of Finance 53(2): 499–547CrossRefGoogle Scholar
  2. Andersen T. G., Bollerslev T. (1998) Answering the skeptics: Yes, standard volatility models do provide accurate forecasts. International Economic Review 39(4): 885–905CrossRefGoogle Scholar
  3. Andersen T. G., Bollerslev T., Diebold F. X., Labys P. (2001) The distribution of realized exchange rate volatility. Journal of the American Statistical Association 96(453): 42–55CrossRefGoogle Scholar
  4. Andersen T. G., Bondarenko O. (2007) Construction and interpretation of model-free implied volatility. In: Nelken I. (eds) Volatility as an asset class. Risk Books, London, pp 141–181Google Scholar
  5. Andersen, T. G., & Bondarenko, O. (2010). Dissecting the market pricing of volatility. Working paper, Northwestern University.Google Scholar
  6. Ang A., Chen J., Xing Y. H. (2006) Downside risk. Review of Financial Studies 19(4): 1191–1239CrossRefGoogle Scholar
  7. Bandorff-Nielsen O. E., Kinnebrock S., Sheppard N. (2010) Measuring downside risk-realized semivariance. In Volatility and Time Series Econometrics 21: 117–137CrossRefGoogle Scholar
  8. Bandorff-Nielsen O. E., Sheppard N. (2004) Power and bipower variation with stochastic volatility and jumps. Journal of Financial Econometrics 2: 1–48CrossRefGoogle Scholar
  9. Black F., Scholes M. (1973) Pricing of options and corporate liabilities. Journal of Political Economy 81(3): 637–654CrossRefGoogle Scholar
  10. Bollerslev T., Tauchen G., Zhou H. (2009) Expected stock returns and variance risk premia. Review of Financial Studies 22(11): 4463–4492CrossRefGoogle Scholar
  11. Britten-Jones M., Neuberger A. (2000) Option prices, implied price processes, and stochastic volatility. Journal of Finance 55(2): 839–866CrossRefGoogle Scholar
  12. Campa J. M., Chang P. H. K., Reider R. L. (1998) Implied exchange rate distributions: Evidence from OTC option markets. Journal of International Money and Finance 17(1): 117–160CrossRefGoogle Scholar
  13. Carr P., Lewis K. (2004) Corridor variance swaps. Risk 17(2): 67–72Google Scholar
  14. Carr P., Madan D. (1998) Towards a theory of volatility trading. In: Jarrow R. (eds) Volatility: New estimation techniques for pricing derivatives. Risk Books, London, pp 417–427Google Scholar
  15. Carr P., Madan D. (2005) A note on sufficient conditions for no arbitrage. Finance Research Letters 2: 125–130CrossRefGoogle Scholar
  16. Carr P., Wu L. (2006) A tale of two indices. Journal of Derivatives, Spring 13(3): 13–29CrossRefGoogle Scholar
  17. Carr P., Wu L. R. (2009) Variance risk premiums. Review of Financial Studies 22(3): 1311–1341CrossRefGoogle Scholar
  18. Coval J. D., Shumway T. (2001) Expected options returns. Journal of Finance 56: 983–1009CrossRefGoogle Scholar
  19. Demeterfi, K., Derman, E., Kamal, M., & Zou, J. (1999). More than you ever wanted to know about volatility swaps. Goldman Sachs quantitative strategies research notes. New York: Goldman Sachs.Google Scholar
  20. Derman E., Kani I. (1994) Riding on a smile. Risk 7(2): 32–39Google Scholar
  21. Diebold F. X., Mariano R. S. (1995) Comparing predictive accuracy. Journal of Business & Economic Statistics 13(3): 253–263Google Scholar
  22. Hansen, C., Christensen, B., & Prabhala, N. (2001). Accounting for the overlapping data problem in the implied-realized volatility regression. Center for analytical finance working paper. University of Aarhus, Aarhus, Denmark.Google Scholar
  23. Hansen P. R., Lunde A. (2006) Consistent ranking of volatility models. Journal of Econometrics 131(1-2): 97–121CrossRefGoogle Scholar
  24. Harvey D., Leybourne S., Newbold P. (1997) Testing the equality of prediction mean squared errors. International Journal of Forecasting 13(2): 281–291CrossRefGoogle Scholar
  25. Jiang G. J., Tian Y. S. (2005) The model-free implied volatility and its information content. Review of Financial Studies 18(4): 1305–1342CrossRefGoogle Scholar
  26. Jiang G. J., Tian Y. S. (2007) Extracting model-free volatility from option prices: An examination of the VIX index. Journal of Derivatives 14(3): 35–60CrossRefGoogle Scholar
  27. Moriggia V., Muzzioli S., Torricelli C. (2009) On the no-arbitrage condition in option implied trees. European Journal of Operational Research 193(1): 212–221. doi: 10.1016/j.ejor.2007.10.017 CrossRefGoogle Scholar
  28. Muzzioli S. (2010a) Option-based forecasts of volatility: An empirical study in the DAX-index options market. European Journal of Finance 16(6): 561–586CrossRefGoogle Scholar
  29. Muzzioli, S. (2010b). Towards a volatility index for the Italian stock market. CEFIN working paper No 23, University of Modena and Reggio Emilia.Google Scholar
  30. Patton, A. (2010). Volatility forecast comparison using imperfect volatility proxies. Journal of Econometrics. doi: 10.1016/j.jeconom.2010.03.034.
  31. Patton, A., Sheppard, K. (2009) Evaluating volatility and correlation forecasts. , Handbook of Financial Time Series.Google Scholar
  32. Poon S. H., Granger C. W. J. (2003) Forecasting volatility in financial markets: A review. Journal of Economic Literature 41(2): 478–539CrossRefGoogle Scholar
  33. Rompolis, L. S., & Tzavalis, E. (2010). Retrieving risk neutral moments and expected quadratic variation from option prices. Working paper, University of Cyprus.Google Scholar
  34. Tsiaras, L. (2009). The forecast performance of competing implied volatility measures: The case of individual stocks. Finance research group working papers.Google Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of Economics and CEFINUniversity of Modena and Reggio EmiliaModenaItaly

Personalised recommendations