Modelling dependency of volatility on sampling frequency via delay equations

Abstract

The paper studies the modelling of time series with the prescribed dependence of the volatility on the sampling frequency. This dependence is often observed for 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.