The authors derive low frequency, say weekly, models implied by high frequency, say daily, ARMA models with symmetric GARCH errors. They show that low frequency models exhibit conditional heteroskedasticity of the GARCH form as well. The parameters in the conditional variance equation of the low frequency model depend upon mean, variance, and kurtosis parameters of the corresponding high frequency model. Moreover, strongly consistent estimators of the parameters in the high frequency model can be derived from low frequency data. The common assumption in applications that rescaled innovations are independent is disputable, since it depends upon the available data frequency.

This paper investigates the effect of closed overnight exchanges on option prices. During the trading day, asset prices follow the literature's standard affine model that allows for stochastic volatility and random jumps. Independently, the overnight asset price process is modeled by a single jump. We find that the overnight component reduces the variation in the random jump process significantly. However, neither the random jumps nor the overnight jumps alone are able to empirically describe all features of option prices. We conclude that both random jumps during the day and overnight jumps are important in explaining option prices, where the latter account for about one quarter of total jump risk.