Market Fear Gauge as the Source of Volatility Asymmetry – A New Perspective

Modelling the asymmetric effect between return and volatility has long been an important issue in finance as well as in econometrics. While much literature interpret this asymmetric effect as a natural result from leverage and modelled as a threshold GARCH process, it has now accepted that it is more likely to due to the feedback effect from expected volatility. Considering this explanation, in this paper we demonstrate a new perspective toward the modelling of asymmetric effect in volatility by incorporating a new volatility expectation factor. The nice feature is that the factor is deduced from the market expectation about future volatility in VIX and constructed as being orthogonal to past information. Therefore, the volatility expectation is distinct from the existing model-based forecasts about future volatility under GARCH or the other volatility models. Our preliminary results shown the prominent role played by the factor of volatility expectation in returns. The asymmetric effect in volatility function prevailing in threshold GARCH models disappears when this new factor is considered. Moreover, we gauge that the popularity of asymmetric GARCH or stochastic volatility models might be attributed to the mis-specification of the mean function where an important variable being missed. We also found the risk premium in terms of the GARCH-M term is no longer significant in index returns after controlling the volatility feedback effect in mean function. Our paper demonstrates a new perspective in modelling the asymmetric volatility feedback effect. We therefore conclude that the past leverage explanation of asymmetry in volatility is likely a misunderstanding due to omitting a relevant variable about expectation of future volatility.