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From Martingales to ANOVA: Implied and Realized Volatility
Feb 8, 2001
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Abstract:
Implied volatility and realized volatility are two different
ways to describe the variations in the price returns of financial data.
Their relationship, however, remains unclear in the literature. In this
research, we establish a theoretical connection between these two types of
volatility. We find that depending on the smoothness level of the
cumulative implied volatility, the implied-realized association can be
represented differently.
Moreover, this relationship can be tested empirically. Using a non-parametric approach and martingale decomposition, on the one hand we are able to obtain estimators for the two variations in price returns. We examine the statistical properties of the procedure -- in particular, how to set confidence intervals -- and we investigate the impact of the estimation scheme on trading error. On the other hand, we can combine our theoretical findings with the ideas of ANOVA in analyzing stock-return variation in incomplete financial markets. This latter method decomposes the variation content implied from an option into two parts: the variation "observed" from historical price returns, and the residual variation |
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2001 Purdue University Last Update: July 10, 2001 Please send comments and suggestions to the Webmaster. |