9. Implied Volatility Indices and ARCH Models

  1. Evdokia Xekalaki and
  2. Stavros Degiannakis

Published Online: 31 MAR 2010

DOI: 10.1002/9780470688014.ch9

ARCH Models for Financial Applications

ARCH Models for Financial Applications

How to Cite

Xekalaki, E. and Degiannakis, S. (2010) Implied Volatility Indices and ARCH Models, in ARCH Models for Financial Applications, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470688014.ch9

Author Information

  1. Department of Statistics Athens University of Economics and Business, Greece

Publication History

  1. Published Online: 31 MAR 2010
  2. Published Print: 16 APR 2010

ISBN Information

Print ISBN: 9780470066300

Online ISBN: 9780470688014



  • ARCH models;
  • explanatory variable;
  • implied volatility indices;
  • VIX index;
  • volatility forecasts


Implied volatility is the standard deviation of the return on the asset, which would have to be fed into a theoretical option pricing formula to yield a theoretical value identical to the price of the option in the marketplace, assuming all other inputs are known. The computation of implied volatility indices takes into account the latest advances in financial theory, eliminating measurement errors that had characterized implied volatility measures. Implied volatility indices appear to eliminate the biases and misspecification problems that characterized the implied volatility measures, they are regarded as informative variables for forecasting the next day’s volatility. Including realized or implied volatility as an explanatory variable in an ARCH model appears to lead to more accurate volatility forecasts. The chapter compares S&P500 log-return one-step-ahead volatility forecasts obtained at time t with and without the incorporation of information on the closing price of the VIX index at time t-1.

Controlled Vocabulary Terms

autoregressive conditional heteroskedasticity; Forecast accuracy; Independent variable