Another look at the implied and realised volatility relation: a copula-based approach

Abstract

The main aim of this paper is to obtain a direct measure of the relation between the future and implied volatilities, in order to determine the appropriateness of using linear modelling to establish the implied–realised volatility relation. To achieve this aim, the dependence structure for implied and realised volatilities is modelled using bivariate standard copulas. Dependence parameters are estimated using a semiparametric method and by reference to three databases corresponding to different assets and frequencies. Two of these databases have been employed in previous research, and the third was constructed specifically for the present study. The first two databases span periods of major crises during the 1980s and 1990s, while the third contains data corresponding to the 2007 financial and economic crisis. The empirical evidence obtained shows that the dependence coefficient is always positive and constant over time, as expected. However, the influence of extreme-volatility events should be taken into account when the data present significant asymmetric tail dependence; models that impose symmetry underestimate the conditional expectation in extreme tail events. Therefore, it might be preferable to model nonlinear conditional expectations to forecast the realised volatility, using implied volatility as a predictor, as is the case with copula models and neural networks.