Measuring and Modelling the Volatility of Financial Time Series

Abstract

The thesis studies the measures and models of volatility for financial time series. We address the dependency of volatility on sampling frequency and show that this relationship can be explained by using delay equations for the underlying prices. In addition, a new implied volatility process is proposed to reduce the impact of the price movement. This allows us to improve the forecast accuracy of future volatility via the heterogeneous autoregressive model and random forest algorithm.