Volatility Forecasts and the At-the-Money Implied Volatility: A Multi-Components ARCH Approach and its Relation with Market Models

  title={Volatility Forecasts and the At-the-Money Implied Volatility: A Multi-Components ARCH Approach and its Relation with Market Models},
  author={Gilles Zumbach},
  • G. Zumbach
  • Published 12 December 2008
  • Business
  • Derivatives
This article explores the relationships between several forecasts for the volatility built from multi-scale linear ARCH processes, and linear market models for the forward variance. This shows that the structures of the forecast equations are identical, but with different dependencies on the forecast horizon. The process equations for the forward variance are induced by the process equations for an ARCH model, but postulated in a market model. In the ARCH case, they are different from the usual… 
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