Modelling Dependency of Volatility on Sampling Frequency via Delay Equations

The paper studies the impact of the sampling frequency on the volatility of financial time series. We suggest to model the dependence of volatility on sampling frequency via delay equations for the underlying prices. It appears that these equations allow to model the price processes with volatility that increases when the sampling rates increase. In addition, these equations are able to model the inverse phenomena where the volatility decreases with the increase in sampling frequencies. We analyse the choice of the parameters for delay equations and discuss how to match these parameters with the historical data