Modeling Dependency of Volatility on Sampling Frequency via Delay Equations

Abstract

The paper studies the modeling 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.

Forecasting of Realised Volatility with the Random Forests Algorithm

“…An additional difficulty is that these parameters are not directly observable; they are defined by the underlying model and by many other factors. For example, it appears that the volatility depends on the sampling frequency and on the delay parameter in the model equation see, e.g., Luong and Dokuchaev (2016). In addition, there is no a unique comprehensive model for stock price evolution; for example, there are many models with stochastic equations for volatility, with jumps, with fractional noise, etc.…”