A Simultaneous Equation Approach on the Relationship between Implied,Realised and Historical Volatility

Abstract

This article investigates the relationship between implied, realised and historical volatility by taking into account measurement errors. In this study, call and put implied volatility is calculated from June 2001 to April 2012, using non-overlapping 131 monthly at-the-money samples. The study shows analyses of predictive power of call and put implied volatility separately using simultaneous equation approach. The present work also accounts for the error-in-variable problem which is controlled using instrumental variable technique. Two-stage least squares (2SLS) and three-stage least squares (3SLS) estimations have been performed in order to obtain the consistent estimate of implied volatility. Instrumental variable estimation procedure uncovers that implied volatility has been measured with error. Indeed, the study also accounts for the endogenous nature of the call and put implied volatility dealing with full information maximum likelihood (FIML) estimation of the entire system. Ordinary least squares (OLS) result shows that call and put implied volatility best subsumes the information about the future volatility. Option prices (implied volatility) are the best forecast for the realised return volatility and useful in the pricing of risky financial assets.

Keywords

2SLS 3SLS FIML historical volatility implied volatility realised volatility simultaneous equation

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