Is the variance swap rate affine in the spot variance? Evidence from S&P500 data

We empirically investigate the functional link between the variance swap rate and the spot variance. Using S&P500 data over the period 2006-2018, we find overwhelming empirical evidence supporting the affine link analytically found by Kallsen et al. (2011) in the context of exponential affine stochastic volatility models. Tests on yearly subsamples suggest that exponential mean-reverting variance models provide a good fit during periods of extreme volatility, while polynomial models, introduced in Cuchiero (2011), are suited for years characterised by more frequent price jumps.