Joint Modeling of Call and Put Implied Volatility

Abstract

This paper exploits the fact that implied volatilities calculated from identical call and put options have often been empirically found to differ, although they should be equal in theory. We propose a new bivariate mixture multiplicative error model and show that it is a good fit to Nikkei 225 index call and put option implied volatility (IV). A good model fit requires two mixture components in the model, allowing for different mean equations and error distributions for calmer and more volatile days. Forecast evaluation indicates that, in addition to jointly modeling the time series of call and put IV, cross effects should be added to the model: put-side implied volatility helps forecast call-side IV, and vice versa. Impulse response functions show that the IV derived from put options recovers faster from shocks, and the effect of shocks lasts for up to six weeks.