Is the Variance Swap Rate Affine in the Spot Variance? Evidence from S&P500 Data

ABSTRACT

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 implied by 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 modelsare suited for years characterized by more frequent price jumps.

KEYWORDS:

• Variance swap
• spot variance
• exponential affine models
• exponential mean-reverting variance models
• polynomial models

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. Note that the estimator by Cuchiero and Teichmann (2015) is also consistent in the presence of jumps in the volatility, which typically occur jointly to jumps in the price, coherently with the so-called leverage effect (see, e.g., the empirical studies on US markets in Jacod and Todorov (2010), Bandi and Renò (2016), Bibinger and Winkelmann (2018)).

Additional information

Funding

S. Scotti acknowledges financial support from the Institut Europlace de Finance grant ‘Clusters and Information Flow: Modelling, Analysis and Implications’ and from a visiting grant received by the University of Florence. Part of the research was completed while M.E. Mancino was visiting the Université de Paris under a visiting funding scheme, which the author acknowledges.