The paper addresses the forecasting of realised volatility for financial time series using the heterogeneous autoregressive model (HAR) and machine learning techniques. We consider an extended version of the existing HAR model with included purified implied volatility. For this extended model,...

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...

The paper studies methods of dynamic estimation of volatility for financial time series. We suggest to estimate the volatility as the implied volatility inferred from some artificial 'dynamically purified' price process that in theory allows to eliminate the impact of the stock price movements....

We consider a market with fractional Brownian motion with stochastic integrals generated by the Riemann sums. We found that this market is arbitrage free if admissible strategies that are using observations with an arbitrarily small delay. Moreover, we found that this approach eliminates the...

We consider fractional Brownian motion with the Hurst parameters from (1/2,1). We found that the increment of a fractional Brownian motion can be represented as the sum of a two independent Gaussian processes one of which is smooth in the sense that it is differentiable in mean square. We...